Question

Suppose that you are obtaining a personal loan from your uncle in the amount of $30,000 (now) to be repaid in three years to cover some of your college expenses. If your uncle usually earns 9% interest (annually) on his money, which is invested in various sources, what minimum lump-sum payment three years from now would make your uncle satisfied with his investment?

Answer 1

To satisfy your uncle's 9% annual interest rate, you would need to repay him a lump-sum payment of $38,850.87 after three years, calculated using the future value of a single lump sum at compound interest: FV = $30,000(1.09)^3.

Step-by-step explanation:

To calculate the minimum lump-sum payment that would satisfy your uncle's expectation of a 9% annual return on his investment, we can use the formula for the future value of a single lump sum at compound interest. The formula is:

FV = PV(1 + i)^n

Where:

• FV is the future value of the loan.
• PV is the present value of the loan, which is $30,000 in this case.
• i is the interest rate per period, which is 9% or 0.09 in decimal form.
• n is the number of periods, which is 3 years in this scenario.

Following these definitions, we can calculate the future value to find out what your repayment amount would be in three years:

FV = $30,000(1 + 0.09)³

Calculating this gives:

FV = $30,000(1.09)³

FV = $30,000(1.295029)

FV = $38,850.87

Therefore, to satisfy your uncle's 9% interest rate, you would need to repay him $38,850.87 in a lump-sum payment after three years.

Answer 2

$38,851 approx

Step-by-step explanation:

As per the information provided in the question, the minimum annual rate of return would be at-least equal to the usual rate of return the investor (here uncle) earns. Here it is 9% per annum.

Anything earned below this rate of return will not satisfy the investor since this represents the minimum required rate of return.

A=
`P(1 + r)^(n)`

Where A= Amount

P= Principal

r= Annual Rate Of Interest

n= period of loan

Therefore, A=
`30,000(1 + .09)^(3)`

A= $38,850.87 or $38,851 approx.