Ans. 1 | We need to calculate the Present value factor for 13th period as the amount dues | |||
in this year (period) . | ||||
*Calculation of Present value factor @5 %. | ||||
Periods | PV @ 5% | |||
1 | 1 / (1 + 0.05)^1 | 0.95238 | ||
2 | 1 / (1 + 0.05)^2 | 0.90703 | ||
3 | 1 / (1 + 0.05)^3 | 0.86384 | ||
4 | 1 / (1 + 0.05)^4 | 0.82270 | ||
5 | 1 / (1 + 0.05)^5 | 0.78353 | ||
6 | 1 / (1 + 0.05)^6 | 0.74622 | ||
7 | 1 / (1 + 0.05)^7 | 0.71068 | ||
8 | 1 / (1 + 0.05)^8 | 0.67684 | ||
9 | 1 / (1 + 0.05)^9 | 0.64461 | ||
10 | 1 / (1 + 0.05)^10 | 0.61391 | ||
11 | 1 / (1 + 0.05)^11 | 0.58468 | ||
12 | 1 / (1 + 0.05)^12 | 0.55684 | ||
13 | 1 / (1 + 0.05)^13 | 0.53032 | ||
Present value = Amount * Present value of 1 factor for 13th period | ||||
$28,000 * 0.53032 | ||||
$14,848.96 | ||||
Ans. 2 | The amount received at the end of each period so we need to calculate the | |||
Present value of an annuity of at 10% | ||||
*Calculation of Present value factor @ 10%. | ||||
Periods | PV @ 10% | |||
1 | 1 / (1 + 0.10)^1 | 0.90909 | ||
2 | 1 / (1 + 0.10)^2 | 0.82645 | ||
3 | 1 / (1 + 0.10)^3 | 0.75131 | ||
4 | 1 / (1 + 0.10)^4 | 0.68301 | ||
5 | 1 / (1 + 0.10)^5 | 0.62092 | ||
6 | 1 / (1 + 0.10)^6 | 0.56447 | ||
Total of Present value of an annuity | 4.35526 | |||
Present value = Amount * Present value of an annuity factor | ||||
$28,000 * 4.35526 | ||||
$121,947.28 | ||||
--- (a) What is the present value of $28,000 due 13 periods from now, discounted at...
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