(Annuity number of periods) Alex Karev has taken out a $190,000 loan with an ann

Question

(Annuity number of periods) Alex Karev has taken out a $190,000 loan with an annual rate of 1i percent compounded monthly to pay off hospital bills from his wife lzzy's illness. If the most Alex can afford to pay is $2,500 per month, how long will it take to pay off the loan? How long will it take for him to pay off the loan if he can pay $3,000 per month? Use five decimal places for the monthly percentage rate in your calculations. a. If Alex can pay $2,500 per month, the number of years it takes for him to pay off the loan isyears. (Round to one decimal place.)

Explanation / Answer

a. If Alex can pay $2,500 per month

We can use following Present Value of an Annuity formula to calculate the time period required to pay the loan

PV of loan = PMT * [1-(1+i) ^-n)]/i

Where,

Present value of loan (PV) =$190,000

Monthly payments PMT =$2,500

Number of installments n =?

Annual interest rate = 11%; therefore Monthly interest rate I =11%/12 =0.91667%

Therefore

$190,000= $2,500 * [1- (1+0.91667%) ^-n]/0.91667%

Or n = 130.73 months or 130.73 /12 = 10.9 years

Now if Alex can pay $3,000 per month

Monthly payments PMT =$3,000 and

$190,000= $3,000 * [1- (1+0.91667%) ^-n]/0.91667%

Or n = 95.21 months or 95.21 /12 = 7.9 years

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