Find the periodic payment method needed to attain the future value of the annuity. Round your answer to the nearest cent. Given that the future value is $7200, rate is 3.5%, time is 5 years compounded quaterly
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11 Answers
To calculate the periodic payment needed to attain a future value, you can use the formula for the future value of a series:
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FV=P×(
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Where:
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r is the interest rate per period,
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n is the number of compounding periods per year,
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t is the number of years.
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P will give you the periodic payment needed
To calculate the periodic payment needed to attain a future value, you can use the formula for the present value of an ordinary annuity. The formula is:
PMT = FV / [(1 + r)^n - 1] / r
Where:
PMT is the periodic payment
FV is the desired future value
r is the interest rate per compounding period
n is the number of compounding periods
By plugging in the values for FV, r, and n into this formula, you can determine the periodic payment required to reach the specified future value. Keep in mind that the interest rate and number of compounding periods should be consistent with each other (e.g., if the interest rate is an annual rate, the number of compounding periods should be expressed in years).
It's important to note that this formula assumes a constant interest rate and equal periodic payments. If your situation involves varying interest rates or irregular payment amounts, different calculations may be necessary.
PMT = FV / [(1 + r)^n - 1] / r
Where:
PMT is the periodic payment
FV is the desired future value
r is the interest rate per compounding period
n is the number of compounding periods
By plugging in the values for FV, r, and n into this formula, you can determine the periodic payment required to reach the specified future value. Keep in mind that the interest rate and number of compounding periods should be consistent with each other (e.g., if the interest rate is an annual rate, the number of compounding periods should be expressed in years).
It's important to note that this formula assumes a constant interest rate and equal periodic payments. If your situation involves varying interest rates or irregular payment amounts, different calculations may be necessary.
To calculate the periodic payment needed to attain a future value, you can use the formula for the future value of an ordinary annuity:
PMT = FV / [(1 + r)^n - 1] * (1 + r)
Where:
PMT = Periodic payment
FV = Future value desired
r = Interest rate per period
n = Number of periods
You will need to know the future value you want to achieve, the interest rate per period, and the number of periods.
For example, let's say you want to accumulate $10,000 in 5 years with an interest rate of 6% per year. Plugging these values into the formula, the calculation would be:
PMT = 10000 / [(1 + 0.06)^5 - 1] * (1 + 0.06)
PMT = 10000 / [1.338225 - 1] * 1.06
PMT = 10000 / 0.338225 * 1.06
PMT = 10000 / 0.3583165
PMT ≈ $27.92
Therefore, to attain a future value of $10,000 in 5 years at an interest rate of 6% per year, you would need to make periodic payments of approximately $27.92.
PMT = FV / [(1 + r)^n - 1] * (1 + r)
Where:
PMT = Periodic payment
FV = Future value desired
r = Interest rate per period
n = Number of periods
You will need to know the future value you want to achieve, the interest rate per period, and the number of periods.
For example, let's say you want to accumulate $10,000 in 5 years with an interest rate of 6% per year. Plugging these values into the formula, the calculation would be:
PMT = 10000 / [(1 + 0.06)^5 - 1] * (1 + 0.06)
PMT = 10000 / [1.338225 - 1] * 1.06
PMT = 10000 / 0.338225 * 1.06
PMT = 10000 / 0.3583165
PMT ≈ $27.92
Therefore, to attain a future value of $10,000 in 5 years at an interest rate of 6% per year, you would need to make periodic payments of approximately $27.92.
To find the periodic payment for an annuity, you can use the future value of an annuity formula:
\[ FV = P \times \left( \frac{(1 + r/n)^{nt} - 1}{r/n} \right) \]
Where:
- \( FV \) is the future value of the annuity (\$7200),
- \( P \) is the periodic payment (what we want to find),
- \( r \) is the annual interest rate (3.5% or 0.035),
- \( n \) is the number of times interest is compounded per year (quarterly means \( n = 4 \)),
- \( t \) is the number of years (5 years).
Let's substitute these values into the formula and solve for \( P \):
\[ 7200 = P \times \left( \frac{(1 + 0.035/4)^{4 \times 5} - 1}{0.035/4} \right) \]
Now calculate this expression to find the periodic payment (\( P \)).
\[ FV = P \times \left( \frac{(1 + r/n)^{nt} - 1}{r/n} \right) \]
Where:
- \( FV \) is the future value of the annuity (\$7200),
- \( P \) is the periodic payment (what we want to find),
- \( r \) is the annual interest rate (3.5% or 0.035),
- \( n \) is the number of times interest is compounded per year (quarterly means \( n = 4 \)),
- \( t \) is the number of years (5 years).
Let's substitute these values into the formula and solve for \( P \):
\[ 7200 = P \times \left( \frac{(1 + 0.035/4)^{4 \times 5} - 1}{0.035/4} \right) \]
Now calculate this expression to find the periodic payment (\( P \)).
For instance, imagine you want to save $10000 in five years To find the periodic payment needed to be used. A financial formula that considers the interest rate and time is required, let's assume an annual interest rate of 5%.
The formula for the future value FV or payment in this scenario is
FV = Pv
(1+r)n
where: FV is the future value ( in this case,$10000)
Pv is the present value( the initial amount you want to save)
r is the interest rate per period (5% or 0.05)
n is the number of periods ( five years)
rearranging the formula to solve for PV, present value, or the periodic payment
PV= 10000
(1+0.05)5
calculating this gives the periodic payment to attain the future value of $10000 in five years.
This example demonstrates the application of financial principles to determine the required periodic payment, showcasing the practicality of understanding and utilizing such calculations in financial planning.
To find the periodic payment needed to attain the future value of the annuity, we can use the formula for the future value of an ordinary annuity:
\[ FV = P \times \left( \frac{{(1 + r)^{nt} -1}}{r} \right) \]
Where:
- \( FV \) = Future Value- \( P \) = Periodic Payment- \( r \) = Interest Rate per period- \( n \) = Number of compounding periods per year- \( t \) = Total number of periodsGiven:
- \( FV = $7200 \)
- \( r =3.5\% \) or \(0.035 \) (converted to decimal)
- \( n =4 \) (compounded quarterly)
- \( t =5 \) yearsPlugging in the values, we get:
\[7200 = P \times \left( \frac{{(1 +0.035)^{4 \times5} -1}}{0.035} \right) \]
\[7200 = P \times \left( \frac{{(1.035)^{20} -1}}{0.035} \right) \]
\[7200 = P \times \left( \frac{{1.808848 -1}}{0.035} \right) \]
\[7200 = P \times \left( \frac{{0.808848}}{0.035} \right) \]
\[7200 = P \times23.1108 \]
To solve for \( P \):
\[ P = \frac{7200}{23.1108} \]
\[ P \approx311.39 \]
Rounding to the nearest cent, the periodic payment needed to attain the future value of the annuity is approximately $311.39.
\[ FV = P \times \left( \frac{{(1 + r)^{nt} -1}}{r} \right) \]
Where:
- \( FV \) = Future Value- \( P \) = Periodic Payment- \( r \) = Interest Rate per period- \( n \) = Number of compounding periods per year- \( t \) = Total number of periodsGiven:
- \( FV = $7200 \)
- \( r =3.5\% \) or \(0.035 \) (converted to decimal)
- \( n =4 \) (compounded quarterly)
- \( t =5 \) yearsPlugging in the values, we get:
\[7200 = P \times \left( \frac{{(1 +0.035)^{4 \times5} -1}}{0.035} \right) \]
\[7200 = P \times \left( \frac{{(1.035)^{20} -1}}{0.035} \right) \]
\[7200 = P \times \left( \frac{{1.808848 -1}}{0.035} \right) \]
\[7200 = P \times \left( \frac{{0.808848}}{0.035} \right) \]
\[7200 = P \times23.1108 \]
To solve for \( P \):
\[ P = \frac{7200}{23.1108} \]
\[ P \approx311.39 \]
Rounding to the nearest cent, the periodic payment needed to attain the future value of the annuity is approximately $311.39.
A number of variables, such as the interest rate, the number of compounding periods in a year, and the time period, affect the periodic payment required to achieve a future value. The formula for determining the present value of an annuity provides the periodic payment (PMT) required to achieve a future value (FV).
PMT=
(
r
(1+r)
nt
−1
)
FV
Whereas
r is the interest rate per period, n is the number of compounding periods per year, t is the number of years, PMT is the periodic payment, and FV is the future value.
Remember that this calculation is based on the assumptions of a constant interest rate and regular payments.
PMT=
(
r
(1+r)
nt
−1
)
FV
Whereas
r is the interest rate per period, n is the number of compounding periods per year, t is the number of years, PMT is the periodic payment, and FV is the future value.
Remember that this calculation is based on the assumptions of a constant interest rate and regular payments.
To find the occasional installment expected to achieve a future worth, you can involve the recipe for the future worth of a series or annuity. The recipe is:
\[ FV = P \times \left( \dfrac{(1 + r)^{nt} - 1}{r} \right) \]
Where:
- \( FV \) is the future worth,
- \( P \) is the occasional installment,
- \( r \) is the financing cost per period,
- \( n \) is the quantity of intensifying time frames each year, and
- \( t \) is the quantity of years.
To tackle for \( P \), you can modify the recipe:
\[ P = \dfrac{FV}{\left( \dfrac{(1 + r)^{nt} - 1}{r} \right)} \]
This recipe computes the intermittent installment expected to accomplish a particular future worth in light of the given loan fee, building recurrence, and time span.
\[ FV = P \times \left( \dfrac{(1 + r)^{nt} - 1}{r} \right) \]
Where:
- \( FV \) is the future worth,
- \( P \) is the occasional installment,
- \( r \) is the financing cost per period,
- \( n \) is the quantity of intensifying time frames each year, and
- \( t \) is the quantity of years.
To tackle for \( P \), you can modify the recipe:
\[ P = \dfrac{FV}{\left( \dfrac{(1 + r)^{nt} - 1}{r} \right)} \]
This recipe computes the intermittent installment expected to accomplish a particular future worth in light of the given loan fee, building recurrence, and time span.