How much must be deposited today in an account earning 6% annually to accumulate a 20% down payment to use in purchasing a car one year from now,assuming that the car's current price is $20,000,and inflation will be 4%?
A) $3,774
B) $3,782
C) $3,925
D) $4,080

Question

Quizplus · Accepted Answer

First, we need to calculate the amount of the down payment. A 20% down payment on a $20,000 car is $4,000.

Next, we need to adjust for inflation. In one year, the price of the car will be $20,800 (20,000 x 1.04 = 20,800). So, we need to save up $4,160 (20% of 20,800) for the down payment.

Finally, we can use the formula for present value of a lump sum:
Present Value = Future Value / (1 + r)^n

where r is the annual interest rate and n is the number of periods. In this case, we have one period (one year). Plugging in the values, we get:

Present Value = 4,160 / (1 + 0.06)^1
Present Value = 3,925

Therefore, we need to deposit $3,925 today to accumulate a 20% down payment for the car one year from now.

How Much Must Be Deposited Today in an Account Earning