Manuel Rios wishes to determine how long it will take an initial deposit of $10,

Question

Manuel Rios wishes to determine how long it will take an initial deposit of $10, 000 to double. If Manuel earns 10% annual interest on the deposit, how long will it take for him to double his money? How long will it take if he earns only 7% annual interest? How long will it take if he can earn 12% annual interest? Reviewing your findings in parts a, b, and c. indicate w hat relationship exists between the interest rate and the amount of time it will take Manuel to double hit money. Manuel assumes that the money will be doubled in five years. Explain why the rate of return is NOT 20 percent per year.

Explanation / Answer

a)

future value = present value * (1+ interest rate)^number of years

number of years = log(futurevalue/presnetvalue) / log(1+interest rate)

10000 * (1+10%)^n = 20000

=>
n = 7.27 years

b)

n = log(2)/log(1.07) = 10.25 years

c)

n = log(2)/log(1.12) = 6.12 years

d)

number of years = log(2) / log(1+interest rate)

e)

since the interest rate is compunded per year , so if tis taking 5 years for money to double then interest rate is less than 20%

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