Question

Birdie Brunella wants ₱5,000 at the end of each 3-month period for the next 6 years. If Birdie’s bank is paying 8% interest compounded quarterly, how much must she deposit now in order to receive the desired ordinary annuity?

Answer 1

Given:

Birdie Brunella wants $5,000 at the end of each 3-month period for the next 6 years. If Birdie’s bank is paying 8% interest compounded quarterly.

We will find the initial deposit should be made now

so,

A = $5,000 * 6 * 12/3 = 120,000

Compunded quarterly, n = 4

Time = 6 years

interest rate = 8% = 0.08

The compounded interest formula is:

$A=P\cdot(1+\frac{r}{n})^{nt}$$\begin{gathered} 120000=P\cdot(1+\frac{0.08}{4})^{4\cdot6}=P\cdot1.6084 \\ \\ P=\frac{120000}{1.6084}=74,606.58 \end{gathered}$

so, the answer will be $74,606.58