Question

5. Finding the interest rate and the number of years

The future value and present value equations also help in finding the interest rate and the number of years that correspond to present and future value calculations.

If a security currently worth $12,800 will be worth $16,843.93 seven years in the future, what is the implied interest rate the investor will earn on the security—assuming that no additional deposits or withdrawals are made?

0.19%

7.60%

1.32%

4.00%

If an investment of $35,000 is earning an interest rate of 12.00%, compounded annually, then it will take     for this investment to reach a value of $81,884.79—assuming that no additional deposits or withdrawals are made during this time.

Which of the following statements is true—assuming that no additional deposits or withdrawals are made?

It takes 10.50 years for $500 to double if invested at an annual rate of 5%.

It takes 14.21 years for $500 to double if invested at an annual rate of 5%.

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.16,843.93=12800*(1+r/100)^7

(16,843.93/12800)^(1/7)=(1+r/100)

(1+r/100)=1.04

r=1.04-1

=4%

b.81,884.79=35000*(1.12)^n

(81,884.79/35000)=(1.12)^n

Taking log on both sides;

log (81,884.79/35000)=n*log 1.12

n=log (81,884.79/35000)/log 1.12

=7.5 years

c.1.A=500*(1.05)^10.5

=500*1.6691203

=$834.56(Approx)

2.A=500*(1.05)^14.21

=500*2

=$1000

Hence the correct option is:

It takes 14.21 years for $500 to double if invested at an annual rate of 5%.