4. Finding the interest rate and the number of years The future value and presen
ID: 2812251 • Letter: 4
Question
4. 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 aurrently worth $2,000 will be worth $2,809.86 three 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? 1.41% o 0.47% 12.00% 7.12% If an investment of $50,000 is earning an interest rate of 4.00%, compounded annually, then it will take for this investment to reach a value of $71,165.59-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%. O It takes 14.21 years for $500 to double if invested at an annual rate of 5%.Explanation / 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.
2809.86=2000*(1+r/100)^3
(2809.86/2000)^(1/3)=(1+r/100)
(1+r/100)=1.12
r=(1.12-1)*100
=12%
2.
We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
71165.59=50000*(1.04)^n
(71165.59/50000)=(1.04)^n
Taking log on both sides;
log (71165.59/50000)=n*log 1.04
n=log (71165.59/50000)/log 1.04
=9 years
3.
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.
A=$500*(1.05)^10.5
=$500*1.669120304
=$834.56(Approx)
b.A=$500*(1.05)^14.21
=$500*2
=$1000(Approx).
Hence the correct option is B.
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