Question

Suppose you have $10,000 to invest. Which investment yields the greater return over 7 years: 6.6% compounded monthly or 6.7% compounded quarterly? A) Both investment plans yield the same return. B) $10,000 invested at 6.6% compounded monthly over 7 years yields the greater return. C) $10,000 invested at 6.7% compounded quarterly over 7 years yields the greater return.

Answer 1

C) $10,000 invested at 6.7% compounded quarterly over 7 years yields the greater return.

Explanation:

-We determine the effective interest rate in both scenarios and use it to calculate the investment's value after 7 years.

#Given n=7yrs, P=$10,000 and i=6.6% compounded monthly:

`i_m=(1+i/m)^m-1\\\\=(1+0.066/12)^(12)-1=0.06803\\\\\therefore A=P(1+i_m)^n\\\\=10000(1.06803)^7\\\\\approx \$15,852.00`

#Given n=7rs, P=10000, i=6.7%

`i_m=(1+i/m)^m-1\\\\=(1+0.067/4)^(4)-1=0.06870\\\\\therefore A=P(1+i_m)^n\\\\=10000(1.06870)^7\\\\\approx \$15,921.75`

Hence, the investment has the largest value($15,921.75) when the interest rate is compounded quarterly.