Question

Twenty years ago, your grandfather deposited $500 in a savings account earning 4% annually, with interest compounded on a quarterly basis. What is that savings account worth today? What would the savings account be worth if interest were compounded monthly?

Answer 1

Compound interest rate formula :

A= P [1 + (r/n)]^nt

where, A = Amount ; P = principal = $500 ; r = interest rate (in decimal) = 4% = 0.04 ; n = number of times interest rate compounded per period = 4 ; t = number of time periods = 20

Therefore, Amount = $500 [ 1 + (0.04/4)]^(4*20)

Or, Amount = $500 (1 + 0.01)⁸⁰

Or, Amount = $1108.36

The savings account is worth $1108.36 today.

If the interest rates were compounded monthly, then n = 12.

Therefore, Amount = $500 [1 + (0.04/12)]^(12*20)

Or, Amount = $1111.29

The savings account would worth $1,111.29