Question 6 666 points You borrowed some money at 8 percent p

Question 6 (6.66 points) You borrowed some money at 8 percent per annum. You repay the loan by making three annual payments of $ 149 (first payment made at t- 1), followed by five annual payments of $ 513,followed by four annual payments of $ 885. How much did you borrow? (Round your answer to 2 decimal places; record your answer without commas and without a dollar sign). Your Answer: Answer

Solution

Total present values of all loan repayment amounts discounted at 8 %, is the loan amount.

Year

Cash flow(C)

PV Factor calculation

PV Factor (F)

PV (=C x F)

1

$149

1/(1+8%)^1

0.925925926

$137.96

2

$149

1/(1+8%)^2

0.85733882

$127.74

3

$149

1/(1+8%)^3

0.793832241

$118.28

4

$513

1/(1+8%)^4

0.735029853

$377.07

5

$513

1/(1+8%)^5

0.680583197

$349.14

6

$513

1/(1+8%)^6

0.630169627

$323.28

7

$513

1/(1+8%)^7

0.583490395

$299.33

8

$513

1/(1+8%)^8

0.540268885

$277.16

9

$885

1/(1+8%)^9

0.500248967

$442.72

10

$885

1/(1+8%)^10

0.463193488

$409.93

11

$885

1/(1+8%)^11

0.428882859

$379.56

12

$885

1/(1+8%)^12

0.397113759

$351.45

NPV

$3,593.62

Hence loan amount is $3,593.62

Borrowed amount 3593.62

Year	Cash flow(C)	PV Factor calculation	PV Factor (F)	PV (=C x F)
1	$149	1/(1+8%)^1	0.925925926	$137.96
2	$149	1/(1+8%)^2	0.85733882	$127.74
3	$149	1/(1+8%)^3	0.793832241	$118.28
4	$513	1/(1+8%)^4	0.735029853	$377.07
5	$513	1/(1+8%)^5	0.680583197	$349.14
6	$513	1/(1+8%)^6	0.630169627	$323.28
7	$513	1/(1+8%)^7	0.583490395	$299.33
8	$513	1/(1+8%)^8	0.540268885	$277.16
9	$885	1/(1+8%)^9	0.500248967	$442.72
10	$885	1/(1+8%)^10	0.463193488	$409.93
11	$885	1/(1+8%)^11	0.428882859	$379.56
12	$885	1/(1+8%)^12	0.397113759	$351.45
			NPV	$3,593.62