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 $786.86 in 10 years.

b. Invest $3,000.00 and receive $10,927.45 in 15 years.

c. Invest $31,180.47 and receive $100,000.00 in 20 years.

d. Invest $31,327.88 and receive $1,000,000.00 in 45 years.

a. What annual rate of return will Keiko earn if she invests $400.00 today and receives $786.86 in 10 years?

​______% (Round to two decimal​ places.)

b. What annual rate of return will Keiko earn if she invests $3,000.00 today and receives $10,927.45 in 15 ​years?

______% (Round to two decimal​ places.)

c. What annual rate of return will Keiko earn if she invests $31,180.47 today and receives $100,000.00 in 20 years?

_____​% (Round to two decimal​ places.)

d. What annual rate of return will Keiko earn if she invests $31,327.88 today and receives $1,000,000.00 in 45 years?

_____​% (Round to two decimal​ places.)

Answer 1

We use the formula:  
A=P(1+r/100)^n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

A.786.86=400*(1+r/100)^10

(786.86/400)^(1/10)=(1+r/100)

(1+r/100)=1.07

r=1.07-1

=7%

b.10,927.45=3000*(1+r/100)^15

(10,927.45/3000)^(1/15)=(1+r/100)

(1+r/100)=1.09

r=1.09-1

=9%

c.100,000=31,180.47*(1+r/100)^20

(100,000/31,180.47)^(1/20)=(1+r/100)

(1+r/100)=1.06

r=1.06-1

=6%

d.1,000,000=31,327.88*(1+r/100)^45

(1,000,000/31,327.88)^(1/45)=(1+r/100)

(1+r/100)=1.08

r=1.08-1

=8%