SOLUTION: A developer needs $80,000 to buy land. He is able to borrow the money at 7% compounded quarterly. How much interest will be paid on the loan if it is paid off in 5 years? (To the n

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Question 430008: A developer needs $80,000 to buy land. He is able to borrow the money at 7% compounded quarterly. How much interest will be paid on the loan if it is paid off in 5 years? (To the nearest dollar, do not include the $)
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
Principal P = 80000
Amount= A
years=n 5
compounded 4 times a year
Rate = 7.00 0.02
Amount = P*((n+r)/n)^n

Amount =80000*( 1+0.02)^5*4
Amount =80000*( 1+0.02)^20
80000*(1.02)^20
Amount =113182.26
Interest =113182.26-80000=33,182

Answer by ikleyn(53742) About Me  (Show Source):
You can put this solution on YOUR website!
.
A developer needs $80,000 to buy land. He is able to borrow the money at 7% compounded quarterly.
How much interest will be paid on the loan if it is paid off in 5 years?
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        The solution by @mananth is irrelevant to the problem and is wholly incorrect
        both conceptually and technically.

        For solving this problem,  standard formulas for loan amortizing should be used. 


Use the standard formula for the loan quarterly payment

    P = L%2A%28r%2F%281-%281%2Br%29%5E%28-n%29%29%29


where L is the loan amount; r = 0.07%2F4 is the effective interest rate per quarter;
n is the number of payments (same as the number of quarters); P is the quarterly payment.


In this problem  L = $80000;  r = 0.07%2F4;  n = 5*4 = 20.


Substitute these values into the formula and get for quarterly payment

    P = 80000%2A%28%28%280.07%2F4%29%29%2F%281-%281%2B0.07%2F4%29%5E%28-20%29%29%29 = $4775.30.


Thus the quarterly payment is $4775.30.


In total, a developer will pay  5*4*4775.30 = 95,506 dollars in 5 years.


The difference $95,506 - $80,000 = $15,506 is the interest the developer pays to financial company.

Solved.

You can check my calculations using any of numerous online loan calculators,
for example, this one https://www.calculator.net/loan-calculator/