How much money must you deposit into a savings account at th

How much money must you deposit into a savings account at the end of each year at 5% interest compounded annually in order to earn $13,157.13 interest during a 15-year period? Can you please break it down step by step so I will know exactly what is being done. Thanks!

Solution

Deposit + Interests = Deposit (1+ interest rate)^Time period => P + I = P(1+r)^t
P + 13,157.13 = P( 1 + 0.05)^15
P = P x 1.05^15 - 13,157.13
P = 2.0789P - 13,157.13
P - 2.0789P = - 13,157.13
-1.0789P = -13,157.13
P = 12194.9485587 = $12195

You must deposit $12195 into a saving account to earn $13157.13 interest