Question

You're trying to save to buy a new $140,000 Ferrari. You have $37,000 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

To calculate the time needed to save for a $140,000 Ferrari with a starting amount of $37,000 at a 5.5% interest rate, use the compound interest formula and solve for 't'. You will need to use logarithms to isolate 't' and find the number of years required to reach your savings goal.

Step-by-step explanation:

To determine how long it will take for you to save enough money to buy a new $140,000 Ferrari with an initial investment of $37,000 at an annual interest rate of 5.5%, you can use the formula for compound interest. This formula is A = P(1 + r/n)^(nt), where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for, in years.

Since we want to find t, we rearrange the formula to solve for t: log(A/P) = n * t * log(1 + r/n) Because the interest is compounded annually, n = 1. We can plug in the values to solve for t: t = log(140,000 / 37,000) / log(1 + 0.055) Using a calculator, you can find the number of years t required to reach your goal.