Question

# (1 pt) A perpetuity will make annual payments, with the first payment coming 9 years from...

(1 pt) A perpetuity will make annual payments, with the first payment coming 9 years from now. The first payment is for 4700 dollars and each payment that follows is 120 dollars more than the one before. If the effective rate of interest is 5.2 percent, what is the present value?

First of all lets find present value of 4700 \$ perpetuity

first payment will start from year 9 , hence we need to find PV of perpetuity at year 8

PV of perpetuity = Annuity/r

r = rate of interest = 5.2%

Thus P of perpetuity = 4700/5.2%

=90385\$

Now we shall calculate PV of 120 \$ perpetuity

first payment will start from year 10 , hence we need to find PV of perpetuity at year 9

PV of perpetuity = Annuity/r

r = rate of interest = 5.2%

Thus P of perpetuity = 120/5.2%

=2308\$

Now let us calculate PV of both perpetuity now

Present value = FV/(1+r)^n

= 90385/(1+5.2%)^8 + 2308/(1+5.2%)^9

=90385/(1+0.052)^8 + 2308/(1+0.052)^9

= 90385/(1.052)^8 + 2308/(1.052)^9

= 90385/1.500 + 2308/1.5781

= 60251.86 + 1462.49

=61714.35 \$

i.e 61714 \$