Question

Suppose you want to buy a car of $ 140,000 after 10 years. To buy it, you will save equal amount of money from the end of this year. How much do you have to save per year? The annual interest rate is 5%

I.

$ 9,854.45

II.

$ 111,30.64

III.

$ 12,696.61

IV.

$ 233,743.5

Answer 1

Answer :- Option II). $ 111,30.64 (approx).

Explanation :- Savings per year = Total amount needed to buy car / Uniform annual compound factor.

= 140000 / 12.57789^{(NOTE 1)}

= $ 111,30.64 (approx).

NOTE 1 :- Uniform annual compound factor = [ (1 + i) ^N - 1 ] / i         (i = interest rate and N = number of years)

= [ (1 + 0.05)¹⁰ - 1 ] / 0.05 (Interest rate = 5 % or 0.05)

= [ (1.05)¹⁰ - 1) / 0.05

= (1.6288946 - 1) / 0.05

= 0.6288946 / 0.05

= 12.57789 (approx).

Conclusion :- Savings needed per year to purchase car in tenth year = $ 111,30.64 (Option II)