Question

How much would you have to invest today to receive:

a. $100,000 in 6 years at 12 percent?

b.$100,000 in 15 years at 12 percent?

c.$10,000 at the end of each year for 25 years at 12 percent

d.$75,000 at the end of each year for 25 years at 12 percent?

Answer 1

a) Here FV = $100,000 , n = 6 years and r = rate of interest = 12%

PV = FV/(1+r)^n

= 100000/(1+12%)^6

= 100000/(1.12)^6

= 100000/1.9738

= 50663.11$

Thus one needs to invest 50663.11$ to get 100,000$ after 6 years at interest rate of 12%

b)

Here FV = $100,000 , n = 15 years and r = rate of interest = 12%

PV = FV/(1+r)^n

= 100000/(1+12%)^15

= 100000/(1.12)^15

= 100000/5.4736

= 18269.63$

Thus one needs to invest 18269.63$ to get 100,000$ after 15 years at interest rate of 12%

c) Here Annuity = $10,000 , n = 25 years and r = rate of interest = 12%

PV = Annuity[ 1- 1/(1+r)^n / r]

= 10000 [1 - 1/(1+12%)^12 / 12% ]

= 10000 [1 - (1/1.12)^12 / 0.12]

= 10000 [1 - 0.2567 / 0.12]

= 10000 [0.7433 / 0.12]

= 10000[6.194374]

= 61943.74 $

Thus one need to invest $ 61943.74 today to get $10,000 at the end of each year for 25 years at 12 percent

d)

Here Annuity = $75,000 , n = 25 years and r = rate of interest = 12%

PV = Annuity[ 1- 1/(1+r)^n / r]

= 75,000 [1 - 1/(1+12%)^12 / 12% ]

= 75,000 [1 - (1/1.12)^12 / 0.12]

= 75,000 [1 - 0.2567 / 0.12]

= 75,000 [0.7433 / 0.12]

= 75,000[6.194374]

= 464578.07 $

Thus one need to invest 464578.07 $ today to get $10,000 at the end of each year for 25 years at 12 percent