Question 430008
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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.



<pre>
Use the standard formula for the loan quarterly payment

    P = {{{L*(r/(1-(1+r)^(-n)))}}}


where L is the loan amount; r = {{{0.07/4}}} 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 = {{{0.07/4}}};  n = 5*4 = 20.


Substitute these values into the formula and get for quarterly payment

    P = {{{80000*(((0.07/4))/(1-(1+0.07/4)^(-20)))}}} = $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.
</pre>

Solved.


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