You’re trying to save to buy a new $215,000 Ferrari. You have $36,000 today that can be invested at your bank. The bank pays 4.3 percent annual interest on its accounts. How long will it be before you have enough to buy the car? (Do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.) Length of time years

42.45 years

Explanation:

Discounting is the means by which the today's value of an amount in the future is computed. Compounding is the process by which the future value of  a present amount is determined. In other words, the present value of $1 tomorrow is determined by discounting while the future value of $1 tomorrow is determined by compounding.

Where

Fv = Pv(1 + r)^n

Fv is the future value

Pv is the present value

r is rate

n is time

215000 = 36000(1 + 0.043)^n

215/36 = 1.043^n

Taking the log of both sides

log (215/36) = log 1.043^n

n = log (215/36) / log 1.043

n = 42.45 years

It will take 42.45 years to have enough to buy the car

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