SOLUTION: 28. Kay is saving $200 a month into an account earning 5% interest. How long will it take her to save $20,000?

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Question 1161707: 28. Kay is saving $200 a month into an account earning 5% interest. How long will it
take her to save $20,000?
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Assume contributions at the end of each month, and interest compounding monthly, the formula for the future value is

A+=+P%28%28%281%2Br%2Fn%29%5E%28nt%29-1%29%2F%28r%2Fn%29%29

A = future value
P = periodic contribution
r = (annual) interest rate
n = # of contributions per year = $ of compounding periods per year
t = # of years

In this problem,
A = 20000
P = 200
r = .05
n = 12
t = to be determined

20000+=+200%28%28%281%2B.05%2F12%29%5E%2812t%29-1%29%2F%28.05%2F12%29%29

The unknown is in an exponent, so you will need to use logarithms or a utility like a graphing calculator.

100+=+%28%28%281.0041667%29%5E%2812t%29-1%29%2F%28.0041667%29%29

0.41667+=+%281.0041667%29%5E%2812t%29-1%29

1.41667+=+%281.0041667%29%5E%2812t%29

ln%28%281.41667%29%29+=+12t%2Aln%28%281.0041667%29%29

t+=+ln%28%281.41667%29%29%2F%2812%2Aln%28%281.0041667%29%29%29

t+=+6.98 to 2 decimal places

ANSWER: 6.98 years.

Since contributions are made monthly, her savings will be a bit over $20,000 after 7 years.