Danny decided to invest his $500 tax refund rather than spending it. He found a bank that would pay him 4% interest, compounded quarterly. If he deposits the entire $500 and does not deposit or withdraw any other amount, how long will it take him to double his money in the account? Round your answer to the nearest tenth of a year. It will take Answer years for his investment to double.

Question

Mathematics

Sullivan Robles

12 June, 03:43

Danny decided to invest his $500 tax refund rather than spending it. He found a bank that would pay him 4% interest, compounded quarterly. If he deposits the entire $500 and does not deposit or withdraw any other amount, how long will it take him to double his money in the account? Round your answer to the nearest tenth of a year. It will take Answer years for his investment to double.

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Answers (1)

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Bridger Barrett · Answer 1

Present value, PV = $500

Future value, FV = 2*PV = 2*500 = $1,000

Rate, r = 4% = 0.04

Compounding times in a year, n = 4 (compounded quarterly)

Time, t = ?

The future value expression is stated as:

FV = PV (1+r/n) ^nt

Substituting;

1000 = 500 (1+0.04/4) ^4t

2 = (1.01) ^4t

ln 2 = 4t ln 1.01

0.6931 = 4t * 0.00995

0.6931 = 0.0398t

t = 17.414 years

Time required for the amount to double is 17.41 years.