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4 A man pays Rs. 4000 at the end of each year for 5 years. The money is worth
6% compounded quarterly He wants to replace it for a payment at the end of each quarter.

A man pays Rs. $4000$ at the end of each year for $5$ years. The money is worth $6\%$ compounded quarterly. He wants to replace it for a payment at the end of each quarter.

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Finance problems

Full solution

Q. A man pays Rs.

4000

at the end of each year for

5

years. The money is worth

6\%

compounded quarterly. He wants to replace it for a payment at the end of each quarter.

Calculate interest rate per quarter: Calculate the interest rate per quarter. $\newline$ Interest rate per annum = $6\%$ $\newline$ Interest rate per quarter = $6\% / 4 = 1.5\%$
Calculate future value of annuity due: Calculate the future value of an ordinary annuity due to the annual payments. $\newline$ Using the formula for the future value of an ordinary annuity: $FV = P \times \left[(1 + r)^n - 1\right] / r$ $\newline$ Where $P =$ annual payment, $r =$ quarterly interest rate, $n =$ total number of quarters. $\newline$ $P = 4000$ , $r = 0.015$ , $n = 5 \times 4 = 20$ quarters $\newline$ $FV = 4000 \times \left[(1 + 0.015)^{20} - 1\right] / 0.015$ $\newline$ $FV = 4000 \times \left[1.34885 - 1\right] / 0.015$ $\newline$ $FV = 4000 \times 0.34885 / 0.015$ $\newline$ $P =$ $0$

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