You want to deposit amounts in the bank at the end of 2011,2012,2013 and 2014,so that you have $1259.71 in your account on 1 January 2015.Calculate how large each of your payments would need to be if the bank compounds quarterly at 8% p.a.
A)$279.56
B)$259.83
C)$284.19
D)$314.93

Question

Quizplus · Accepted Answer

To find the equal payments, we use the future value of an annuity formula: $FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)$, where $FV$ is the future value, $P$ is the payment, $r$ is the interest rate per period, and $n$ is the total number of payments. Given an 8% annual interest rate compounded quarterly, $r = 0.08/4 = 0.02$ (2% per quarter). The deposits are made at the end of each year from 2011 to 2014, so there are 4, 3, 2, and 1 periods until the dates of each deposit to January 1, 2015, respectively. The future value is $1259.71. We solve for $P$ in the equation $1259.71 = P \times \left( \frac{(1 + 0.02)^4 - 1}{0.02} + \frac{(1 + 0.02)^3 - 1}{0.02} + \frac{(1 + 0.02)^2 - 1}{0.02} + \frac{(1 + 0.02)^1 - 1}{0.02} \right)$. Solving this equation gives $P \approx $279.56$.

You Want to Deposit Amounts in the Bank at the End