Question

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

Answer 1

You will have $172,984.44

Answer 2

$172,984.44

Explanation:

We can use the formula

`A = P(1 + (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 * 30 = 120`

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

`1 + r/n = 1.01625`

`(1 + r/n)^(nt) = 1.01625^(120)`

Therefore

`A = 25000 * 1.0625^(120) = 172,984.44`