A loan of 43000 is made at 375 interest compounded annually

A loan of

$43,000

is made at

3.75%

interest, compounded annually. After how many years will the amount due reach

$53,000

or more? (Use the calculator provided if necessary.)

Write the smallest possible whole number answer.

Solution

The formula for annual compound interest is

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

Where:

A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for

53000=43000(1+0.0375)^t

=> 1.0375^t = 1.233

=> t= 5.689 years