Question

For each of the following questions be sure to create a list that outlines the values for N, C/Y-P/Y, I/Y, P.V., and F.V., as well as to show any subsequent calculations.

A) A debt can be paid by payments of $2000 scheduled today, $2000 scheduled in three years, and $2000 scheduled in six years. What single payment would settle the debt four years from now if money is worth 2.3% compounded monthly? (Display the scenario on a “timeline” for full marks)

B) Interest of $6083.19 was charged on a student loan of $30,000 that was compounding semiannually for three years. If the interest rate (rounded to 2 decimal places) remains the same, how long (in years and months) will it take the new total of the loan to accumulate additional interest of at least $6000?

Answer 1

As per question a debt can be paid by payments of $2000 scheduled today, $2000 scheduled in three years, and $2000 scheduled in six years with 2.3% compounded monthly. Thus

PV = $2000

C/Y = 12

P/y = 0

I/Y = 2.3%

FV = $ 2000 with n = 3, and FV 2000 with n = 6.

Taking all the cash flows to 4 year time period

= 2000*(1+0.023/12)^12*4 + 2000*(1+0.023/12)^12 + 2000/(1+0.023/12)^12*2

= 2000*1.0963 + 2000*1.0232 + 2000*0.9551 = $ 6,149.20. Thus a single payment of $ 6,149.20 can be made at the end of 4 year to payoff the loan