Question

In: Math

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

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.)

Solutions

Expert Solution

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).


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