Question

1. Dana needs to make some house repairs in three years that will cost $8,000. She has some money in an account earning 6% annual interest. How much money needs to be in the account today so she will have enough to pay for the repairs?

2. Unfortunately, Dana doesn't have enough money in her account right now. She needs to make additional contributions at the end of each of the next three years to be able to pay for the repairs. Her account currently has $3,500, which, along with her additional contributions, is expected to continue earning 6% annual interest. If she makes equal contributions each year, how large must each contribution be for Dana to have $8,000 after three years?

Answer 1

1. Expected Future Requirement = $8,000

Interest rate = 6% p.a = r n=3

Future Value = Present Principal (1+r)^n

8,000 = P (1+0.06)^3

P = 8,000 / (1+0.06)^3

= 6,716.95 =6,717(Approx) required for her to meet the repair in future

2.

Amount available in her account now=3500

After three years the present amount will be 3500(1.06)^3= 4169 (rounded off)

The balance amount required to meet the repair = 8,000 - 4,169= 3,831

If amount 'x' deposited at the end of first year, @6% pa for next 2 years( investment is made at the end of the each period)

x(1+0.06)^2=1.06^2 x= 1.1236x

Like wise , at the end of second year the same amount  'x' deposited for next one year

x(1.06)^1=1.06x

the same amount  'x' deposited in the last year( it will not generate any interest, as the investment is made at the end of the third year)

Then remaining amount required to contribute equally during the three years to meet the repair will be

1.1236x + 1.06x +x = 3831

x(1.1236+1.06+1) = 3831

3.1836 x = 3831

x = 3831/3.1836 = 1203.35 (Each year Dana has to contribute this amount )

In this case Dana required to have total of 3500+(1203.35 3) = 7110 (Rounded off)

(Assumed that the Dana required the amount for repair after three years, as per the direction by the question)

Case 1. she require 6717 and in case 2 she require 7110. (which is 393 more contribution than the first case)