Question

Finding the interest rate and the number of yearsThe 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.

1. If a security currently worth $12,800 will be worth $17, 983.08 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?

a. 3.20%

b. 1.22%

c. 0.24%

d. 4.00%

2. If an investment of $50,000 is earning an interest rate of 12.00%, compounded annually, then it will take how many years for this investment to reach a value of $98691.13 - assuming that no additional deposits or withdrawal are made during this time?


3. Which of the following statements is true assuming that no additional deposits or withdrawal are made?

a. An investment of $25 at an annual rate of 10% will return a higher value in five years than $50 invested at an annual rate of 5% in the same time

b. An investment of $50 at an annual rate of 5% will return a higher value in five years than $25 invested at an annual rate of 10% in the same time

Answer 1

A=P(1+r/100)^n

where

A=future value

P=present value

r=rate of interest

n=time period.

a.

16843.93=12800*(1+r/100)^7

(16843.93/12800)^(1/7)=(1+r/100)

(1+r/100)=1.04

r=1.04-1

=4%

b.

50618.88=45,000*(1.04)^n

(50618.88/45,000)=(1.04)^n

Taking log on both sides;

log (50618.88/45,000)=n*log 1.04

n=log (50618.88/45,000)/log 1.04

=3 years

c.

1.A=$50*(1.05)^5

=$63.81(Approx).

A=$25*(1.1)^5

=$40.26(Approx).

2.

A=$25*(1.1)^5

=$40.26(Approx).

A=$50*(1.05)^5

=$63.81(Approx).

Hence Case 1 is correct.

Step-by-step explanation: