Question

As part of your financial planning, you wish to purchase a new car five years from today. As of today, the car costs $14000, and the bank has agreed to provide loans. Consider the following situations to estimate the actual cost of the vehicle: 1. Calculate the price of the car after five years if the interest rate for every six months is 3% and compounded monthly. 2. Estimate the value of the vehicle after five years if the quarterly interest rate is 4% and compounded monthly.

Answer 1

Solution:

The current value of the car = $14,000

We need to calculate the future value of the car and we can use Coumpound interest formula to calculate the same .

A = P * ( 1+r)^n

Part 1)

Interest rate for 6 months = 3% hence monthly interest rate = 3% / 6 = 0.5% per month

n = period = 5 years = 5* 12 = 60 months

P = $14,000

A = 14000* ( 1+0.5%) ^ 60 = 14000 * 1.34885= 18,883.9

Price of the car after five years = $18,883.9

Part 2 )

Interest rate per quarter = 4%

Monthly interest = 4% /3 = 1.33333%

n = 60 months

A = 14000* ( 1+1.33333%) ^ 60 = 14000* 2.213807 = $30,993.3

Price of the car after 5 years = $30,993.3