Question

1- Serena Willis will invest $27,700 today. She needs $42,972 in 9 years.

What annual interest rate must she earn?

2- Gary Bautista needs $27,000 in 3 years.

What amount must he invest today if his investment earns 12% compounded annually? What amount must he invest if his investment earns 12% annual interest compounded quarterly? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.)

Investment at 12% annual interest, compounded quarterly ?

Answer 1

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.

42,972=27700*(1+r/100)^9

(42,972/27700)^(1/9)=(1+r/100)

(1+r/100)=1.05

r=1.05-1

=5%(Approx)

2.At 12% compounded annually:

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

27000=P*(1.12)^3

P=27000/(1.12)^3

=27000*0.71178

=$19218(Approx)

At 12% annual interest compounded quarterly:

We use the formula:
A=P(1+r/4)^4n
where
A=future value
P=present value
r=rate of interest
n=time period.

27000=P*(1+0.12/4)^(4*3)

P=27000/(1+0.12/4)^(4*3)

=27000*0.70138

=$18937(Approx).