Question

Suppose you want to borrow $95,000 and you find a bank offering a 20-year loan with an APR of 79 a. Find your regular payments if you pay n 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 n- 1 would be s The payment for n - 12 would be s The payment for n- 26 would be s The payment for n- 52 would be s (Do not round until the final answer. Then round to the nearest cent as needed.)

Answer 1

according to given information Principal amount    P = $ 95000

Period   n = 20 years

Rate of interest r = 7%

Rate of interest r = 7 / 100 = 0.07

Now we can use the below formula to find the annual payment (PMT)

PMT = [ p x r x (1+r)ⁿ ] / [(1+r)ⁿ-1]

Case (1)

If n = 1 that means payments made on yearly basis then for 20 years n = 20 x1 = 20

PMT = [95000 x 0.07 x (1+0.07)²⁰ ] / [(1+0.07)²⁰-1]

PMT = [6650 x 3.86968] / [3.86968 - 1]

PMT = [25733.4016] / [2.86968]

PMT = $8967.3418 ~ 8967.35

So annaul payment is $ 8967.35

Case (2)

If n = 12 that means payments made on monthly basis then for 20 years n = 20 x12 = 240

Then rate of interest r = 0.07 / 12 = 0.005833

PMT = [95000 x 0.005833 x (1+0.005833)²⁴⁰ ] / [(1+0.005833)²⁴⁰-1]

PMT = [554.135 x 4.03841] / [4.03841 - 1]

PMT = [2237.8285] / [3.03841]

PMT = $736.513 ~ 736.5

So monthly payment is $ 736.5

Case (3)

If n = 26 that means payments made on biweekly basis then for 20 years n = 20 x26 = 520

And rate of interest r = 0.07/26 = 0.002692

PMT = [95000 x 0.002692 x (1+0.002692)⁵²⁰ ] / [(1+0.002692)⁵²⁰-1]

PMT = [255.74 x 4.042737] / [4.042737 - 1]

PMT = [1033.8895] / [3.042737]

PMT = $339.78

So biweekly payment is $ 339.78

Case (4)

If n = 52 that means payments made on weekly basis then for 20 years n = 20 x52 = 1040

And rate of interest r = 0.07/52 = 0.001346

PMT = [95000 x 0.001346x (1+0.001346)¹⁰⁴⁰ ] / [(1+0.001346)¹⁰⁴⁰-1]

PMT = [127.87 x 4.05073] / [4.05073 - 1]

PMT = [517.9676] / [3.05073]

PMT = $169.7848 ~ 169.79

So weekly payment is $ 169.79

(b) so we need to compute the total payout amount for each case

So total payout amount = payment amount x number of payments

Case (1) : annual payment

total payout amount = 8967.35 x 20

                                                = $179347

Case (2) : monthly payment

total payout amount = 736.5 x 240

                                                = $176760

Case (3) : biweekly payments

total payout amount = 339.78 x 520

                                                = $176685.6

Case (4) : weekly payment

total payout amount = 169.79 x 1040

                                                = $176581.6

Part c : when we compare all the payments in all cases we can observe payout amount is decreasing gradually. So when the number of payments increase then total payout amount will decrease.