Answer the following short questions. Use MARR = 12% and tax rate = 40% in all...

Answer the following short questions. Use MARR = 12% and tax rate = 40% in all problems unless otherwise specified.

3. A young engineer calculated that monthly payments of $A are required to pay off a $5000 loan for n years at i% interest, compounded monthly. If the engineer decides to borrow $10,000 instead, her monthly payments are $2A. True or False

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Expert Solution

3. The answer is True.

If we properly analyse we can see that during the first instance The engineer has borrowed $5000 for 'n' Years at and interest rate of 'i%'. His monthly repayment was $A.

Again The engineer borrowed $10000 for the same 'n' years and again the same Interest 'i%'. He will definitely have to repay the double amount it is $2A.

The repayment amount is double because the borrowed amount has been doubled. There is no change in the Number of years for repayment and the Rate of Interest.

Let us see with an example -

Loan amount $5000, Duration - 5 years = 60 months, Interest rate - 5% = 0.0512= 0.0041

M = (P r(1+r)ⁿ) (1+r)ⁿ - 1

= (5000 0.0041(1+0.0041)⁶⁰) (1+ 0.0041)⁶⁰ - 1

= (5000 0.0041(1.2785)) (1.2785 - 1)

= 5000 0.005240 0.2785

= 5000 0.018831 = $94.15 will be the monthly repayment.

Again the Loan amount is $10000 Duration - 5 years = 60 months, Interest rate = 5% = 0.0512 = 0.0041

We can put $10000 in the above calculations.

= (10000 0.0041(1+0.0041)⁶⁰ ) (1+0.0041)⁶⁰ - 1

= (10000 0.0041(1.2785)) (1.2785 - 1)

= 10000 0.005240 0.02785

= 10000 0.018831 = $188.31 will be the monthly repayment.

Rahul Sunny answered 1 year ago

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