Question

SOLVE BY HAND:

Kevin invested $2000 for 4 years at an annual rate of 10%. Assume there is an annual inflation rate of 4% (first two years) and 6% for (last two years). Currently, a Gucci jacket is worth $2060, and the price is increasing at the rate of inflation each year.

i) Will Kevin be able to purchase/afford the jacket after 4 years?

ii) If Kevin were to pay tax at a rate of 50%, will he be able to purchase the Gucci jacket at the end of 4 years?

Answer 1

Whenever an investment of $ A earns x% per year, then compounding makes its value at the end of n years =

A*(1+x)^n

Investment's worth after 4 years = 2000*1.1^4 = $2928.20

Due to inflation, the price inrceases. The future value after n years is = Present value*(1+inflation rate)^n

Price of Gucci Jacket at the end of 4 years = 2060*(1.04^2)*(1.06^2)=$2503.4887

i) Thus, the investment worth is more than price of jacket at the end of 4 years. 2928.2>2503.4887. Thus, he would be able to purchase/afford the jacket.

ii) Tax will be paid on the amount of interest earned. Value of investment after 4 years was $2928.20. Amount invested was $2000. Thus, interest earned is (Value of investment after interest - Value of investment made initially)

=(2928.20-2000) = $928.20

50% tax will have to be paid on this amount. Thus, tax paid = 0.50*928.20 = $464.1

Thus, net money left with Kevin = Value of investment - Tax paid = $2928.20-464.1 = $2464.1

Price of jacket is $2503.4887. As the price is more than value of investment left with Kevin, he wont be able to purchase/afford the jacket at the end of 4 years.

In case of any query, write a comment. Thanks!