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 ​$400.00 and receive ​$859.27 in 10 years. b.  Invest ​$3800.00 and receive ​$10,156.24 in 16 years. c.  Invest ​$31,742.91 and receive ​$120,000.00 in 20 years. d.  Invest ​$34,653.91 and receive ​$1,100 comma 000.00 in 30 years. a.  What annual rate of return will Keiko earn if she invests ​$400.00 today and receives ​$859.27 in 10 ​years? ​ (Round to two decimal​ places.)

Answer 1

a.Information provided:

Present value= $400

Future value= $859.27

Time= 10 years

The question is solved by calculating the yield to maturity.

The annual rate of return is calculated by entering the below in a financial calculator:

PV= -400

FV= 859.27

N= 10

Press the CPT key and I/Y to compute the annual rate of return.

The value obtained is 7.9461.

Therefore, the annual return on the investment is 7.95%.

b.Information provided:

Present value= $3,800

Future value= $10,156.24

Time= 16 years

The question is solved by calculating the yield to maturity.

The annual rate of return is calculated by entering the below in a financial calculator:

PV= -3,800

FV= 10,156.24

N= 16

Press the CPT key and I/Y to compute the annual rate of return.

The value obtained is 6.3370.

Therefore, the annual return on the investment is 6.34%.

c.Information provided:

Present value= $31,742.91

Future value= $120,000

Time= 20 years

The question is solved by calculating the yield to maturity.

The annual rate of return is calculated by entering the below in a financial calculator:

PV= -31,742.91

FV= 120,000

N= 20

Press the CPT key and I/Y to compute the annual rate of return.

The value obtained is 6.8751.

Therefore, the annual return on the investment is 6.88%.

d.Information provided:

Present value= $34,653.91

Future value= $1,100,000

Time= 30 years

The question is solved by calculating the yield to maturity.

The annual rate of return is calculated by entering the below in a financial calculator:

PV= -34,653.91

FV= 1,100,000

N= 30

Press the CPT key and I/Y to compute the annual rate of return.

The value obtained is 12.2160.

Therefore, the annual return on the investment is 12.22%.