Question

Interest rate​ (with changing​ years). Keiko is looking at the following investment choices and wants to know what annual rate of return each choice produces. a. Invest ​$420.00 and receive ​$769.05 in 12 years. b. Invest ​$3 comma 000.00 and receive ​$11 comma 567.45 in 14 years. c. Invest ​$32 comma 303.47 and receive ​$110 comma 000.00 in 20 years. d. Invest ​$32 comma 275.63 and receive ​$1 comma 100 comma 000.00 in 40 years. a. What annual rate of return will Keiko earn if she invests ​$420.00 today and receives ​$769.05 in 12 ​years? nothing​% ​ (Round to two decimal​ places.)

Answer 1

Answer:

a. 5.18%;

b. 10.12%;

c. 6.32%;

d. 9.22%.

Explanation:

We apply the formula of Annual rate of return to calculate for the four cases.

The formula for calculating annual rate of return as below:

Annual rate of return = $\sqrt[year]{Ending value/Beginning value}$ -1 ;

So, for each of the case given, by applying the formula, the detailed calculations for each case will be:

+ For case a :

$\sqrt[12]{769.5/420} -1$ = 5.18%;

+ For case b:

$\sqrt[14]{11,567.45/3,000} -1$ = 10.12%;

+ For case c:

$\sqrt[20]{110,000/32,303.47} -1$ = 6.32%;

+ For case d:

$\sqrt[40]{1,100,000/32,275.63} -1$ = 9.22%.