a.
Year (n) | Amount paid | DF = 1/(1+r)^n r=0.059 | Present value = Amount paid * DF | Cumulative Presen vale |
0 | 650 | 1.00 | 650.00 | 650.00 |
1 | 650 | 0.94 | 613.79 | 1,263.79 |
2 | 650 | 0.89 | 579.59 | 1,843.38 |
3 | 650 | 0.84 | 547.30 | 2,390.68 |
4 | 650 | 0.80 | 516.81 | 2,907.49 |
5 | 650 | 0.75 | 488.02 | 3,395.50 |
6 | 650 | 0.71 | 460.83 | 3,856.33 |
7 | 650 | 0.67 | 435.15 | 4,291.48 |
8 | 650 | 0.63 | 410.91 | 4,702.39 |
9 | 650 | 0.60 | 388.02 | 5,090.41 |
10 | 650 | 0.56 | 366.40 | 5,456.80 |
11 | 650 | 0.53 | 345.99 | 5,802.79 |
12 | 650 | 0.50 | 326.71 | 6,129.50 |
13 | 650 | 0.47 | 308.51 | 6,438.01 |
14 | 650 | 0.45 | 291.32 | 6,729.33 |
15 | 650 | 0.42 | 275.09 | 7,004.42 |
16 | 650 | 0.40 | 259.76 | 7,264.18 |
17 | 650 | 0.38 | 245.29 | 7,509.47 |
18 | 650 | 0.36 | 231.63 | 7,741.10 |
19 | 650 | 0.34 | 218.72 | 7,959.82 |
20 | 650 | 0.32 | 206.54 | 8,166.35 |
20 | 650 | 0.32 | 206.54 | 8,372.89 |
NPV | 8,372.89 | |||
here we have calculated the present value of the $650 paid every year for the next 21 years. the discounting factor is calculated by taking r= 5.9% and cumulative present value is calculated , by adding the present value of all the previous years and current year.
this is calculated to see in which year will the present value exceeds $7000. which happens in year 16, for whose the present value id $7264. so the answer is d, 16 years.
b.
Future value =Present Value * (1 + interest rate%)^n |
n= tenor |
here , Present value= $24 |
Tenor (n)= 392 |
interest rate= 4.5% or 0.045 |
so substituting all the values, FV= 24* (1+0.045)^392 |
FV= 74,78,20,036.24 |
So as per the calculations above , the answer is a. $74,78,20,036.24
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