Question

Topic : Time value money
Subject : Engineering economics

Today is January 1st 2020 (Year 0), Mr. Solid decided to purchase the Hellcat Confederate X132 on January 2030. The price for Hellcat Confederate X132 in January 2020 is $500k without considering the road-tax. The price is expected to increase by 10% by the time of purchase without any interest rate/inflation. Determine the amount of which Mr. Saran needs to accumulate if he is planning to invest $100k every year starting from the noted Year 0 in order to purchase the motorcycle with road-tax. The road-tax is 50% of the price of the motorcycle for the particular year. Will the amount accumulated be sufficient by the time he would want to make purchase? Take i = 10%.

Answer 1

Given Data

Present cost as on Jan 2020 = $500000

Road Tax rate = 50%

Annuity amount (Planning to invest) = $100000

Interest amount = I = 10%

Solution:

Let us find out the cost of the motorcycle in the future (Jan 2030) at the time of buying it. Inclusive of an increase in the price by 10% and a road tax.

Cost of the motorcycle (Jan 2030) = 500000 + 0.1*500000 + 0.5*500000

Cost of the motorcycle (Jan 2030) = $800000

On the contrary let us estimate how much he will be accumulating as on Jan 2030 by saving $100000 at a rate of 10% for 10 years.

Future worth of savings (Jan 2030) = 100000(F/A,i%,n)

Future worth of savings (Jan 2030) = 100000(F/A,10%,10)

Using DCIF Tables

Future worth of savings (Jan 2030) = 100000(15.937)

Future worth of savings (Jan 2030) = $1593700

Based on the above calculations Mr. Saran will have sufficient amount to make the purchase