Suppose you want to borrow $120,000 and you find a bank offering a 20-year loan

Question

Suppose you want to borrow

$120,000

and you find a bank offering a 20-year loan with an APR of

4%.

a. Find your regular payments if you pay

nequals=1,

12, 26, 52 times a year.

b. Compute the total payout for each of the loans in part (a).

c. Compare the total payouts computed in part (b).

a. The payment for

nequals=1

would be

$nothing.

The payment for

nequals=12

would be

$nothing.

The payment for

nequals=26

would be

$nothing.

The payment for

nequals=52

would be

$nothing.

(Do not round until the final answer. Then round to the nearest cent as needed.)

Explanation / Answer

This can be easily solved using the PMT function in MS Excel with the syntax PMT(rate, nper, pv) , where rate is the interest rate divided by the number of payments in a year, nper is the total number of payments, and pv is the principal amount

borrowed.

(a) nequals = 1, so we have rate = 0.04, nper=20, pv = 120,000

Using the above formula we have the EMI = $8,829.81

nequals = 12, so we have rate = 0.04/12, nper=12x20=240

EMI = $727.18

nequals = 26, rate = 0.04/26, nper = 26x20 = 520

EMI = $335.42

nequals = 52, rate = 0.04/52, nper = 52x20 = 1040

EMI = $167.67

(b) the total payouts can be calculated by multiplying the EMI with nper. So we have:

nper = 1, total payout = $176,596.20

nper = 12, total payout = $174,522.33

nper = 26, total payout = $174,420.28

nper=52, total payout = $174,376.52

(c) So we can conclude that by increasing the number of payments made, or EMI, we wcan reduce the total payouts made.

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