You want to buy a Nissan 300ZX on your 27th birthday.You have priced these cars and found that they currently sell for $30,000.You believe that the price will increase by 5 percent per year until you are ready to buy.You can presently invest to earn 14 percent.If you just turned 20 years old,how much must you invest at the end of each of the next 7 years to be able to purchase the Nissan in 7 years?

Question

Quizplus · Accepted Answer

First, we need to calculate how much the car will cost in 7 years.

Price in 7 years = $30,000 * 1.05^7 = $42,015.94

Next, we need to calculate how much we need to invest at the end of each year to have $42,015.94 in 7 years. We can use the formula for the future value of an annuity:

FV = PMT * (((1 + r)^n - 1) / r)

Where: 
FV = future value 
PMT = payment (what we need to invest each year) 
r = interest rate per period 
n = number of periods

In this case, we need to invest for 7 years and our interest rate is 14% per year, so our interest rate per period is 14%/12 = 1.1667%.

FV = $42,015.94 
r = 1.1667% 
n = 7

PMT = FV / (((1 + r)^n - 1) / r) 
PMT = $42,015.94 / (((1 + 1.1667%)^7 - 1) / 1.1667%) 
PMT = $3,933.93

Therefore, the answer is B) $3,933.93

You Want to Buy a Nissan 300ZX on Your 27th