Tom Nelson invested $9,000 into an account yielding 6%. How long must he leave the money in the account to obtain $12,060.90?
A)2 years
B)3 years
C)4 years
D)5 years

Question

Quizplus · Accepted Answer

To find out how long Tom Nelson must leave his money in the account to obtain $12,060.90 from an initial investment of $9,000 at a 6% annual interest rate, we can use the formula for compound interest, which 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, and t is the time the money is invested for in years. Since the problem does not specify the compounding period, we'll assume it's compounded annually (n = 1). We're solving for t, and we want A to be $12,060.90, P is $9,000, r is 6% or 0.06, and n is 1.Rearranging the formula to solve for t gives us t = log(A/P) / n[log(1 + r/n)]. Plugging in the numbers: t = log(12,060.90/9,000) / log(1 + 0.06), which simplifies to t = log(1.34) / log(1.06). Calculating this gives a value slightly over 4 but less than 5, meaning the money must be left in the account for more than 4 years to reach the desired amount. Since interest is typically compounded at the end of each year and you cannot reach the desired amount in exactly 4 years, you need to leave the money in the account for 5 years to exceed the target amount of $12,060.90.

Tom Nelson Invested $9,000 into an Account Yielding 6