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A person invests 2000 dollars in a bank. The bank pays 6.25% interest compounded semi-annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 5900 dollars?

User Engern
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1 Answer

3 votes

9514 1404 393

Answer:

17.6 years

Explanation:

The compound interest formula is useful for figuring this out.

A = P(1 +r/n)^(nt) . . . . . interest r compounded n per year for t years

Filling in the given values and solving for t, we have ...

5900 = 2000(1 +.0625/2)^(2t)

2.95 = 1.03125^(2t) . . . . divide by 2000, simplify

log(2.95) = 2t×log(1.03125) . . . . take logarithms

t = log(2.95)/(2×log(1.03125) . . . . divide by the coefficient of t

t ≈ 17.6

The person must leave the money in the bank for 17.6 years.

User Lzydrmr
by
7.2k points
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