Question #74230

On Monday, Karuna borrows Rs. 1,00,000 at 8 percent annual interest with repayment to be made in monthly installments for 30 years. Overnight, the market interest rate increases to 12 percent. The lender, anxious to get its money back from Karuna so that it can be loaned out at the higher interest rate, makes Karuna the following offer: if she will double her monthly payment ( this significantly reducing the term of he loan) the lender will reduce the interest rate on the loan to 6 percent per year. Should Karuna take this offer ? Explain. ( Hint : Karuna's Opportunity cost is 12 percent per year. That is, she can invest at the same rate that the back can lend.)

Expert's answer

If Karuna borrows Rs. 100,000 at 8 percent annual interest with repayment to be made in monthly installments for 30 years, then the total amount to be paid is:

100,000*1.08^30 = Rs. 1,006,265.7,

The monthly payment is Rs. 2,795.2.

If the lender offers Karuna to double her monthly payment at reduced interest rate of 6 percent per year, then:

100,000*1.06^t = 2*2,795.2*12t,

1.49*1.06^t = t,

t = 1.65

So, Karuna will repay the loan in 1 year 7 month, so Karuna should take this offer.

100,000*1.08^30 = Rs. 1,006,265.7,

The monthly payment is Rs. 2,795.2.

If the lender offers Karuna to double her monthly payment at reduced interest rate of 6 percent per year, then:

100,000*1.06^t = 2*2,795.2*12t,

1.49*1.06^t = t,

t = 1.65

So, Karuna will repay the loan in 1 year 7 month, so Karuna should take this offer.

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