SOLUTION: You invest $20,000 in a retirement plan. The plan is expected to have an annual return of 12%. Write a rule for the amount of money available at the beginning of the nth year. What

Algebra ->  Sequences-and-series -> SOLUTION: You invest $20,000 in a retirement plan. The plan is expected to have an annual return of 12%. Write a rule for the amount of money available at the beginning of the nth year. What      Log On


   

Question 1034183: You invest $20,000 in a retirement plan. The plan is expected to have an annual return of 12%. Write a rule for the amount of money available at the beginning of the nth year. What is the balance of the account at the beginning of the 20th year?
Found 2 solutions by Theo, robertb:
Answer by Theo(13342) About Me  (Show Source):
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f = p * (1+r)^n

f is the future value
p is the present value
r is the interest rate per time period.
n is the number of time periods.

with annual compounding (1 compounding period per year), r = .12
with p = 20,000, the formula becomes f = 20,000 * 1.12^n

at the beginning of the 20th year, the amount in the account will be f = 20,000 * 1.12^20 = 192,925.8619


Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
At the beginning of the 20th year, 19 years have passed, and so, t = 19.
==> A+=+P%281%2Br%2Fn%29%5E%28nt%29 ==> A+=+20000%281%2B0.12%2F1%29%5E%281%2A19%29+=+20000%2A1.12%5E19
= $172,255.23.