Question

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? 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

(1) PV = Present Value =12800

FV = Future Value = 17983.08

n = Period = 3 years

r = Interest rate = ???

Future value = PV (1+r)^n

17983.08 = 12800 (1+r)^3

(1+r)^3 = 17983.08/12800 = 1.4049

1+r = cube root of 1.4049

1+r = 1.12

r = 1.12-1 = 0.12 or 12%

(2) PV = Present Value = 50000

FV = Future Value = 98691.13

n = Period = ???

r = Interest rate = 12%

Future value = PV (1+r)^n

98691.13 = 50000 (1+0.12)*n

(1.12)^n = 98691.13/50000 = 1.9738226

n = 6 Years

(To check answer please redo the Future value equation inserting n=6)

(3) Future value = PV (1+r)^n

investment of $25 at an annual rate of 10% for5 year = 25 (1+0.10)^5 =25*(1.61051)= 40.26

investment of $50 at an annual rate of 5% for5 year = 50(1+0.05)^5 = 50*(1.27628) =63.81

hence Option 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 is the true statement