Question

Ten years ago, you gave Jen $10,000   in exchange for her promise to give you $28,390 today. What compound annual rate of return was Jen promising? Unfortunately, today Jen told you that he can only give you $8000. If you get the $8000 today, what compound annual rate of return will you earn over the ten-year period?

Answer 1

Given the following information,

Scenario 1:

10 years ago,

Present value PV = $10,000

Future value FV = $28,390

Annual time period t = 10

Annual rate of return = r = ?

We know that the present value is given by the following formula,

PV = FV/ (1+r)^t

Where

PV = Present Value

FV = Future Value

r = rate of return

t = time period

Substituting the given values, we get

10,000 = 28,390/ (1+r)^10

(1+r)^10 = 28,390/ 10,000

(1+r)^10 = 2.8390

(1+r) = 2.8390^(1/10)

(1+r) = 2.8390^(0.1)

1+r = 1.1100

r = 1.1100 - 1

r = 0.1100

r = 11%

Therefore, rate of return when you gave 10,000, 10 years ago for the value of 28,390 today is 11%

Scenario 2:

Present value PV = $10,000

Future value FV = $8,000

Annual time period t = 10

Annual rate of return = r = ?

We know that the present value is given by the following formula,

PV = FV/ (1+r)^t

Where

PV = Present Value

FV = Future Value

r = rate of return

t = time period

Substituting the given values, we get

10,000 = 8000/ (1+r)^10

(1+r)^10 = 8000/ 10,000

(1+r)^10 = 0.8000

(1+r) = 0.8000^(1/10)

(1+r) = 0.8000^(0.1)

1+r = 0.9779

r = 0.9779 - 1

r = -0.0221

r = -2.21%

Therefore, rate of return when you gave 10,000, 10 years ago for the value of 8000 today is -2.21%