In: Finance
Leonore wants to ask for Fidelio’s hand in marriage. She is able
to pay $250 at the end of each month for 6 years. If the interest
rate is 8 percent annually with monthly compounding (an APR), how
much can she afford to borrow to purchase Fidelio an engagement
ring?
A. $1,450.23
B. $2,394.33
C. $5,230.03
D. $7,483.00
E. $10,001.99
F. $14,258.63
G. $16,154.54
H. $79,320.94
I. None of the above
Solution:- | |||||
Annual rate of interest | =8% | ||||
Equal monthly payment | =$250 | ||||
Payment to be made for | 6 years | ||||
Number of peroid in months | =6*12 months | ||||
=72 months | |||||
Compounding rate of interest per month | =0.66666666% | ||||
The amount of loan that she can take | |||||
=Equal monthly installment*PVIFA(0.66666%,72) | |||||
=$250*57.034 | |||||
=$14,258.50 | |||||
ie: "F" | |||||
Working note for refrence :- | |||||
Calculation of PVIF | |||||
peroid | PVIF @0.66666% | ||||
1 | 0.99337749 | ||||
2 | 0.986798838 | ||||
3 | 0.980263753 | ||||
4 | 0.973771946 | ||||
5 | 0.967323132 | ||||
6 | 0.960917025 | ||||
7 | 0.954553342 | ||||
8 | 0.948231803 | ||||
9 | 0.941952128 | ||||
10 | 0.935714041 | ||||
11 | 0.929517265 | ||||
12 | 0.923361528 | ||||
13 | 0.917246557 | ||||
14 | 0.911172083 | ||||
15 | 0.905137836 | ||||
16 | 0.899143552 | ||||
17 | 0.893188965 | ||||
18 | 0.887273812 | ||||
19 | 0.881397832 | ||||
20 | 0.875560766 | ||||
21 | 0.869762357 | ||||
22 | 0.864002347 | ||||
23 | 0.858280483 | ||||
24 | 0.852596511 | ||||
25 | 0.846950183 | ||||
26 | 0.841341247 | ||||
27 | 0.835769456 | ||||
28 | 0.830234564 | ||||
29 | 0.824736327 | ||||
30 | 0.819274503 | ||||
31 | 0.813848849 | ||||
32 | 0.808459127 | ||||
33 | 0.803105099 | ||||
34 | 0.797786527 | ||||
35 | 0.792503178 | ||||
36 | 0.787254818 | ||||
37 | 0.782041215 | ||||
38 | 0.776862139 | ||||
39 | 0.771717362 | ||||
40 | 0.766606656 | ||||
41 | 0.761529796 | ||||
42 | 0.756486557 | ||||
43 | 0.751476717 | ||||
44 | 0.746500055 | ||||
45 | 0.741556351 | ||||
46 | 0.736645387 | ||||
47 | 0.731766945 | ||||
48 | 0.726920811 | ||||
49 | 0.722106771 | ||||
50 | 0.717324612 | ||||
51 | 0.712574122 | ||||
52 | 0.707855093 | ||||
53 | 0.703167316 | ||||
54 | 0.698510583 | ||||
55 | 0.69388469 | ||||
56 | 0.689289432 | ||||
57 | 0.684724605 | ||||
58 | 0.68019001 | ||||
59 | 0.675685445 | ||||
60 | 0.671210711 | ||||
61 | 0.666765612 | ||||
62 | 0.66234995 | ||||
63 | 0.65796353 | ||||
64 | 0.65360616 | ||||
65 | 0.649277647 | ||||
66 | 0.644977799 | ||||
67 | 0.640706427 | ||||
68 | 0.636463343 | ||||
69 | 0.632248358 | ||||
70 | 0.628061287 | ||||
71 | 0.623901945 | ||||
72 | 0.619770148 | ||||
Total | =57.034 |