Your uncle wants to help you with your college expenses,and he promised to pay you $10,000 next year and $15,000 in two years.The current interest rate is 6%,and you expect that this interest rate will be the same for the next year and will increase to 8% in the year after.What is the formula that you should use to compute the present discounted value of your uncle's contribution to your education expenses?

Question

Quizplus · Accepted Answer

The formula for computing the present discounted value is to divide each future payment by the corresponding discount factor, which is (1+r)^t, where r is the interest rate and t is the number of years until the payment is received. In this case, the first payment of $10,000 is due in one year, so its discount factor is 1/(1+0.06)^1 = 0.9434. The second payment of $15,000 is due in two years, so its discount factor is 1/(1+0.06)^2 = 0.8900. However, in the second year the interest rate increases to 8%, so the second discount factor should be based on this rate, which gives a discount factor of 1/(1+0.08)^1 = 0.9259. Therefore, the present discounted value of the payments is: 10,000/0.9434 + 15,000/(0.8900*0.9259) = $23,080.16.

Your Uncle Wants to Help You with Your College Expenses,and