Calculate the present value of an annuity with monthly deposits of $2,000 at 5% for 20 years.
Discuss how the present value of an annuity will change if the deposit is doubled?
PV of annuity = P[{1-(1+r)^-n}/r]
P= Periodic payment= $2000
r= rate of interest= 5% P/a = 5/12% per Month
n= number of period= 240 Months
PV= 2000[{1-(1+0.00417)^-240}/0.00417]
=2000[0.6316/0.00417]
=2000 * 151.463
=$302,926
If the deposit is double
PV= 4000[{1-(1+0.00417)^-240}/0.00417]
=4000* 151.463
=$605,852
SOLUTION :
PV is calculated using following formula :
PV = A((1 + r)^n - 1) / (r * (1 + r)^n)
Where,
A = Annuity = 2000 ($)
r = monthly rate = 5/12 % = 5/1200 = 1/240
=> 1 + r = 241/240
n = number of periods in months = 20*12 = 240
So,
PV
= 2000((241/240)^240 - 1) / ((1/240) * (241/240)^240)
= 303050.63 ($) (ANSWER)
If annuity A is doubled keeping other things unchanged,
the PV also gets doubled to $606101.25(ANSWER).
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