Question

Solve for the unknown number of years in each of the following: (Do not round intermediate...

Solve for the unknown number of years in each of the following: (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

 Present Value Years Interest Rate Future Value \$ 750 9 % \$ 1,605 2,441 7 4,200 33,805 12 392,120 33,500 19 213,332

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,

1605=750*(1.09)^n

(1605/750)=(1.09)^n

Taking log on both sides;

log (1605/750)=n*log 1.09

n=log (1605/750)/log 1.09

=8.83 years(Approx).

b,

4200=2441*(1.07)^n

(4200/2441)=(1.07)^n

Taking log on both sides;

log (4200/2441)=n*log 1.07

n=log (4200/2441)/log 1.07

=8.02 years(Approx).

c.

392120=33805*(1.12)^n

(392120/33805)=(1.12)^n

Taking log on both sides;

log (392120/33805)=n*log 1.12

n=log (392120/33805)/log 1.12

=21.63 years(Approx).

d.

213,332=33500*(1.19)^n

(213,332/33500)=(1.19)^n

Taking log on both sides;

log (213,332/33500)=n*log 1.19

n=log (213,332/33500)/log 1.19

=10.64 years(Approx).

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