Question

You're trying to save to buy a new $230,000 Ferrari. You have $32,000 today that can be invested at your bank. The bank pays 5.5 percent annual interest on its accounts. How long will it be before you have enough to buy the car?

Answer 1

37 years

Step-by-step explanation:

We know,

Future value = Present value (1 + r)^n

Given,

Future value, FV = $230,000;

Present value, PV = $32,000;

Interest rate, r = 5.5% = 0.055;

We have to determine how many years later I can purchase the Ferrari.

Now, putting the values into the formula, we get,

FV = PV × (1 + r)^n

or, $230,000 = $32,000 × (1 + 0.055)^n

or, $230,000 ÷ $32,000 = (1 + 0.055)^n

or, 7.1875 = (1 + 0.055)^n

or, log 7.1875 = n × log 1.055

or, n × log 1.055 = log 7.1875 [Changing the side]

or, n = log 7.1875 ÷ log 1.055

Using financial calculator/Scientific Calculator,

or, n = 0.8566 ÷ 0.0233

Therefore, n = 36.76 or almost 37 years.