Someone invests a constant stream of $450 per year at a continuously compounding interest rate of 5%. What is the present value
1 answer:
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Answer:
PVxa = $27,132.00, PVya = $26,413.00,
Explanation:
Present value (PV) is the value of the future expected cash flow. PV rests on the idea that the worth of a cash received is more than that of the cash promised to be received in the future. To calculate PV a stream of incomes to be received a number of period in the future, the following formula is used:
Where PV = present value
C = cash flow amount from the investment
r = discount rate
n = number of period, in this case years, to receive the cash flow.
The PV formula above is therefore employed to answer the question as follows:
<u>Answer to question (a) </u>
<em>For Investment X in question (a)</em>
PVxa = $4,200 * {[1-(1+r)^-n]/r}
PVxa = $4,200 * {[1-(1+0.05)^-8]/0.05}
PVxa = $4,200 * 6.463212759
PVxa = $27,145.49
<em>For Investment Y in question (a)</em>
PVya = $6,100*{[1-(1+r)^-n]/r}
PVya = $6,100*{[1-(1+0.05)^-5]/0.05}
PVya = $6,100 * 4.329476671
PVya = $26,409.81
<u>Answer to question (b) </u>
<em>For Investment X in question (b)</em>
PVxb = $4,200 * {[1-(1+r)^-n]/r}
PVxb = $4,200 * {[1-(1+0.15)^-8]/0.15}
PVxb = $4,200 * 4.487321508
PVxb = $18,846.75
<em>For Investment Y in question (b)</em>
PVyb = $6,100*{[1-(1+r)^-n]/r}
PVyb = $6,100*{[1-(1+0.15)^-5]/0.15}
PVyb = $6,100 * 3.352155098
PVyb = $20,448.15
Where PVxa, PVya, PVxb and PVyb represents PV for X and Y in questions (a) and (b).
Decisions:
1. In question (a) part where the PV of $27,145.49 of X is greater than $26,409.81 of investment Y, it is better to invest on investment X.
2. In question (b) part where the PV of $20,448.15 of Y is now greater than $18,846.75 of investment X, it is better to invest on investment Y.