Question

This exercise is designed to be solved using technology such as calculators or computer spreadsheets.

You borrow $18,000 with a term of four years at an APR of 8%. Make an amortization table. How much equity have you built up halfway through the term? (Round your answer to two decimal places.)

Answer 1

Since the payment is to be monthly, we presume that interest is to be compounded at monthly intervals.

The formula for computing the loan balance (B) of a fixed payment loan of $ L , for n months at a monthly interest rate r, after p months is B = L[(1 + r)ⁿ - (1 + r)^p]/[(1 + r)ⁿ - 1]. Here, L = 18000, n = 4*12 = 48 , p = 2*12 = 24 and r = (8/100)*(1/12) = 8/1200 = 1/150. Hence, B = 18000[(1+1/150)⁴⁸-(1+1/150)²⁴]/ [(1+1/150)⁴⁸-1] = 18000*(1.375666101-1.172887932)/ (0.375666101) = 18000*(0.202778169)/ (0.375666101) = $ 9716.09 ( on rounding off to the nearest cent). Thus, the equity built up halfway through the term is $ 18000-$ 9716.09   = $ 8283.91.

Note:

The formula for computing the monthly payment (P) for a loan of $ L, for n months at a monthly interest rate r is P = L[r(1 + r)ⁿ]/[(1 + r)ⁿ - 1]. Here, L = 18000, n = 4*12 = 48 , and r = (8/100)*(1/12) = 8/1200 = 1/150. Then, P = (18000)[(1/150)(1+1/150)⁴⁸]/[ (1+1/150)⁴⁸-1] = 120 *(1.375666101)/(0.375666101) = $ 439.43 ( on rounding off to the nearest cent).