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

Respuesta :

Answer:

Option 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 is the true statement

Explanation:

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 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 is the true statement

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