Question

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?

Answer 1

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

Answer 2

If the present value is $2000, the interest rate is 5% and the time period is 20 years, what is the future value?

Answer 3

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).