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 ​$641.99 in 11 years. b.  Invest ​$2,600.00 and receive ​$11,749.06 in 17 years. c.  Invest ​$31,217.27 and receive ​$100,000.00 in 24 years. d.  Invest ​$33,920.59 and receive ​$1,100,000.00 in 35 years.

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.

641.99=450*(1+r/100)^11

(641.99/450)^(1/11)=(1+r/100)

(1+r/100)=1.0328

r=1.0328-1

=3.28%(Approx).

b.

11749.06=2600*(1+r/100)^17

(11749.06/2600)^(1/17)=(1+r/100)

(1+r/100)=1.0928

r=1.0928-1

=9.28%(Approx).

c.

100,000=31,217.27*(1+r/100)^24

(100,000/31,217.27)^(1/24)=(1+r/100)

(1+r/100)=1.0497

r=1.0497-1

=4.97%(Approx).

d.

1,100,000=33,920.59*(1+r/100)^35

(1,100,000/33,920.59)^(1/35)=(1+r/100)

(1+r/100)=1.1045

r=1.1045-1

=10.45%(Approx).