Question

If you deposit $25,000 now at 6.5% compounded quarterly, how much will you have in 30 years?

Answer 1

Answer:

$172,984.44

Step-by-step explanation:

We can use the formula

$A = P(1 + \frac{r}{n})^{nt}$ to compute the final amount

Here P is the principal amount, the original deposit = $25,000

r is the annual interest rate = 6.5% = 0.065 in decimal

n is the number of times the compounding takes place. Here it is quarterly so it is 4 times a year

t is the number of time periods ie 30 years

A is the accrued amount ie principal + interest

Computing different components,

$nt = 4 \times 30 = 120$

$r/n = 0.065/4 = .01625$

$1 + r/n = 1.01625$

$(1 + r/n)^{nt} = 1.01625^{120}$

Therefore

$A = 25000 \times 1.0625^{120} = 172,984.44$