Question

You want to buy your dream car which will cost you $5700. If you could invest your entire savings of $3400 at an annual interest of 10.4%, how long (in years rounded to two decimal places) would you have to wait until you have accumulated enough money to buy the car? Your Answer: Answer Question 14 (1 point) What is the future value (in \$) of cash flows 1−3 at the end of year 3 , assuming a 5% interest rate (compounded annually)?

Answer 1

To find out how long it will take for an investment to reach a desired amount with compound interest, use the future value compound interest formula and solve for time. The variables include the principal amount, annual interest rate, number of times interest is compounded per year, and the future value sought.

Step-by-step explanation:

To calculate how long you need to wait for your savings to grow to a certain amount with compound interest, you can use the formula for compound interest, which is A = P(1+r/n)^(nt). Here, A represents the future value of the investment/loan, 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, and t is the time the money is invested or borrowed for, in years.

Given the details in the question, you have a principal amount of $3400, an annual interest rate of 10.4%, compounded annually (n = 1), and you want the future value to be $5700. Plugging the values into the formula and solving for t, you would do:

$5700 = $3400(1+0.104/1)^(1t)

To find t, you would take the natural logarithm of both sides and solve, which should give you t rounded to two decimal places. Remember, the formula for compound interest is a powerful tool for understanding how investments can grow over time.