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 ​$450.00 and receive ​$654.36 in 11 years.

b.  Invest $3,400.00 and receive ​$11,512.78 in 15 years.

c.  Invest ​$30,409.03 and receive ​$120,000.00 in 28 years.

d.  Invest ​$31,675.39 and receive ​$1,000,000.00 in 35 years.

Answer 1

Future Value = present Value * (1+r)^n

Answer a)

654.36 = 450 * (1+r)^11

(1+r)^11 = 645.36 / 450

(1+r)^11 = 1.43413333333

1+r = 1.43413333333^1/11

r = 1.0333213718 -1  

r = 3.33%

Answer b)

11512.78 =3400 * (1+r)^15

(1+r)^15 =11512.78 / 3400

(1+r)^15 = 3.3861117647

1+r = 3.3861117647^1/15

r = 1.08470943875 -1  

r = 8.47%

Answer c)

120000 = 30409.03 * (1+r)^15

(1+r)^28 =120000 / 30409.03

(1+r)^28 = 3.94619624499

1+r = 3.94619624499^1/28

r = 1.05024856225 -1  

r = 5.02%

Answer d)

1,000,000 = 31675.39 * (1+r)^35

(1+r)^35 =1,000,000/ 31675.39

(1+r)^35 = 31.5702505951

1+r = 31.5702505951^1/35

r = 1.10366308114 -1  

r = 10.37%