Question

5. 1 points HarMathAp12 6.3.041. My Notes Ask Your Teacher Suppose a recent college graduate's first job allows her to deposit $250 at the end of each month in a savings plan that earns 9%, compounded monthly. This savings plan continues for 9 years before new obligations make it impossible to continue. If the accrued amount remains in the plan for the next 15 years without deposits or withdranals how much money will be in the account 24 years after the plan began? (Round your answer to the nearest cent.) $ Need Help? Read It Talk to a Tutor

Answer 1

ANSWER:

I = 9% per year or 9% / 12 per month = 0.75% per month

n = 9 years or 9 * 12 = 108 months

fv = monthly savings(f/a,i,n)

fv = 250(f/a,0.75%,108)

fv = 250 * 383.06

fv = 41,370.81

so at the end of 9 years the account will have $41,370.81

fv at the end of 24 years :

n = (24 - 9) = 15 years or 15 * 12 = 180 months

pv = $41,370.81

fv = ?

i = 0.75%

fv = pv * (1 + i) ^ n

fv = 41,370.81 * (1 + 0.75%) ^ 180

fv = 41,370.81 * (1.0075) ^ 180

fv = 41,370.81 * 3.838

fv = 158,782.94

so at the end of 24 years the account will have $158,782.94