Question

Cal Lury owes $25,000 now. A lender will carry the debt for four more years at 10 percent interest. That is, in this particular case, the amount owed will go up by 10 percent per year for four years. The lender then will require that Cal pay off the loan over the next 12 years at 13 percent interest. What will his annual payment be

Answer 1

$6,185.31

Step-by-step explanation:

Value of debt at end of 4 years = $25,000 * (1 + 10%)^4

Value of debt at end of 4 years = $25,000 * (1.10^4)

Value of debt at end of 4 years = $25,000 * 1.4641

Value of debt at end of 4 years = $36,602.50

Let x be the annual payments

x * [1 - (1 + 13%)^-12] / 13% = $36,602.50

x * [1 - (1.13)^-12] / 13% = $36,602.50

x * [1 - 0.2307059] / 13% = $36,602.50

x * 0.7692941/0.13 = $36,602.50

x * 5.91764692 = $36,602.50

x = $36,602.50/5.91764692

x = 6185.313266375142

x = $6,185.31

So therefore, his annual payment will be $6,185.31.