Question

Francisco has a savings account balance of $2033.88. The interest rate on the account is 2.9% compounded monthly. If he opened the account nine years ago, what was the value of his initial deposit?

Answer 1

The equation for this is:

F = P(1+i)ⁿ
where
F is the present accounts balance
P is the initial deposit
i is the interest rate
n is the number of months

The interest rate is nominal which is 2.9% per year compounded monthly. Since there are 12 months in a year, that is equal to an effective interest rate of 0.24167% per month compounded monthly (i = 0.0024167). In 9 years, there are a total of 108 months, so n=108.

$2033.88 = P(1+0.0024167)¹⁰⁸
P = $1567.147