Question

Miguel deposits 4320 dollars in an account, and 4 years later the account balance is 8140 dollars. If interest is compounded monthly, what is the rate of interest per month?

Answer 1

about 1.33% per month

Explanation:

The future value is given by ...

FV = P(1 +r)^n

where P is the principal, r is the monthly interest rate, and n is the number of months. Solving for r, we get ...

FV/P = (1 +r)^n . . . . . . . divide by P

(FV/P)^(1/n) = 1 +r . . . . . take the n-th root

r = (FV/P)^(1/n) -1 . . . . . subtract 1

Filling in the given numbers, we have ...

r = (8140/4320)^(1/48) -1 ≈ 0.013286 ≈ 1.33%

The rate of interest per month is about 1.33%.