Fred wants to take out a loan. He can afford to make monthly payments of 100 dollars and wants to pay the loan off after exactly 20 years. What is the maximum amount that Fred can afford to borrow if the bank charges interest at an annual rate of 10 percent, compounded monthly

$10,390.96

Explanation:

The formula for the principal amount is

P = A (1 - (1-r)^n / r)

From the given data, A = 100

r =  10 / 100 * 12 = 10 / 1200 = 0.0083

n= 20 * 12 = 240

Now substitute this data in the formula

P = 100 ( 1 - (1 + 0.0083)^-240 / 0.0083)

P = 100 ( 1 - (1/7.27016) / 0.0083)

P = 100 ( 1 - 0.13755 / 0.0083)

P = 100 ( 0.86245 / 0.0083)

P = 100 * 103.90964

P = $10,390.964

P = $10,390.96

The maximum amount that Fred can afford to borrow if the bank charges interest at an annual rate of 10 percent, compounded monthly is $10,390.96

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