Question

If an investment of $45,000 is earning an interest rate of 4.00%, compounded annually, then it will take ______ for this investment to reach a value of $53,686.18—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?

A) 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.

B) 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.

Answer 1

question 1)

time taken is 4.5 years at the given rate (calculation in sheet attached below)

question 2)

statement 1 validation

we know future value = present value *(1+r)^n

future value of 50 in 5 years at 5% rate = 50*(1.05)^5 = 63.81

future value of 25 in 5 years at 10% rate = 25*(1.1)^5 = 40.26

so 50 invested at 5% has more value than 25 invested at 10%

so statement 1 is true