finance question?
John will receive a trust fund when he turns 18 years old 19 months from now. The current balance is $8500 and the fund earns 7% interest compounded monthly. He wishes to buy a boat and he can afford $110 each month on a loan to finance it. How much can he borrow at 4.25% interest, if he wishes to be able to pay off the balance of the loan when he receives his trust fund?
Public Comments
- First let's see what the trust fund will be worth in 19 months. 7% interest compounded monthly means he is paid 7/12% interest each month. In 19 months his balance will be $8,500(1+.07/12)^19 = $9,493.22 He wants to borrow some amount B so that after 19 months of paying $110 at 4.25% monthly the balance will be equal to his trust fund balance of $9,493.22. Let i = .0425/12 Let v = 1/(1+i) v is a present value factor so multiply v^n by the cash flow in the 19th period to calculate its present value. The sum of all the present values is the total present value. B = $110v + $110v^2 + ... + $110v^19 + $9,493.22v^19 B = $110(v + v^2 + ... + v^19) + $9,493.22v^19 B = $110(1-v^19)/i + $9,493.22v^19 v^19 = 1/(1+.0425/12)^19 = 0.935 B = $110(1-0.935)/(0.0425/12) + $9,493.22(0.935) B = $2,018.82 + $8,876.16 B = $10,894.98 Hopefully that's the right answer.
