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The amount of an annuity due consisting of 15 annual payments invested at 8% effective is ` 10,000. Find the size of each payment.?
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The amount of an annuity due consisting of 15 annual payments invested...
Calculation of Annuity Due
An annuity due is a series of payments made at the beginning of each period, instead of at the end of each period. To calculate the annuity due, we need to use the formula:
A = R [(1+i)^n - 1]/i (1+i)
where A is the annuity due, R is the regular payment, i is the interest rate per period, and n is the number of periods.
Given Information
We are given that the amount of the annuity due consisting of 15 annual payments invested at 8% effective is ` 10,000.
Calculating Interest Rate per Period
To calculate the interest rate per period, we need to use the formula:
i = (1 + r/n)^n - 1
where r is the effective annual rate and n is the number of periods in a year. In this case, r = 8% and n = 1 (since the payments are annual).
i = (1 + 0.08/1)^1 - 1 = 0.08
Therefore, the interest rate per period is 8%.
Calculating Regular Payment
Using the formula for annuity due, we can calculate the regular payment:
A = R [(1+i)^n - 1]/i (1+i)
` 10,000 = R [(1+0.08)^15 - 1]/0.08 (1+0.08)
Simplifying this expression, we get:
R = ` 10,000 x 0.08 (1+0.08)/[(1+0.08)^15 - 1]
R = ` 10,000 x 0.08 (1.08)/10.063
R = ` 866.67 (approx.)
Therefore, the size of each payment is ` 866.67 (approx.).
An annuity due is a series of payments made at the beginning of each period, instead of at the end of each period. To calculate the annuity due, we need to use the formula:
A = R [(1+i)^n - 1]/i (1+i)
where A is the annuity due, R is the regular payment, i is the interest rate per period, and n is the number of periods.
Given Information
We are given that the amount of the annuity due consisting of 15 annual payments invested at 8% effective is ` 10,000.
Calculating Interest Rate per Period
To calculate the interest rate per period, we need to use the formula:
i = (1 + r/n)^n - 1
where r is the effective annual rate and n is the number of periods in a year. In this case, r = 8% and n = 1 (since the payments are annual).
i = (1 + 0.08/1)^1 - 1 = 0.08
Therefore, the interest rate per period is 8%.
Calculating Regular Payment
Using the formula for annuity due, we can calculate the regular payment:
A = R [(1+i)^n - 1]/i (1+i)
` 10,000 = R [(1+0.08)^15 - 1]/0.08 (1+0.08)
Simplifying this expression, we get:
R = ` 10,000 x 0.08 (1+0.08)/[(1+0.08)^15 - 1]
R = ` 10,000 x 0.08 (1.08)/10.063
R = ` 866.67 (approx.)
Therefore, the size of each payment is ` 866.67 (approx.).
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The amount of an annuity due consisting of 15 annual payments invested at 8% effective is ` 10,000. Find the size of each payment.?
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The amount of an annuity due consisting of 15 annual payments invested at 8% effective is ` 10,000. Find the size of each payment.? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The amount of an annuity due consisting of 15 annual payments invested at 8% effective is ` 10,000. Find the size of each payment.? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The amount of an annuity due consisting of 15 annual payments invested at 8% effective is ` 10,000. Find the size of each payment.?.
The amount of an annuity due consisting of 15 annual payments invested at 8% effective is ` 10,000. Find the size of each payment.? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The amount of an annuity due consisting of 15 annual payments invested at 8% effective is ` 10,000. Find the size of each payment.? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The amount of an annuity due consisting of 15 annual payments invested at 8% effective is ` 10,000. Find the size of each payment.?.
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