You have $11,000 and will invest the money at an interest rate of .33 percent per month until the account is worth $17,200. How many years do you have to wait until you reach your target account value?Multiple Choice9.89 years11.51 years10.55 years12.18 years11.31 years
Question
You have 17,200. How many years do you have to wait until you reach your target account value?Multiple Choice9.89 years11.51 years10.55 years12.18 years11.31 years
Solution
To solve this problem, we need to use the formula for compound interest, which is:
A = P(1 + r/n)^(nt)
Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = the time the money is invested for in years
In this case, we are given: P = 17,200 r = .33 percent per month = .0033 per month = .0033*12 = .0396 per year (since we need the annual rate) n = 1 (since interest is compounded annually)
We need to find t (time in years). So we rearrange the formula to solve for t:
t = log(A/P) / (n * log(1 + r/n))
Substituting the given values:
t = log(17200/11000) / (1 * log(1 + .0396/1)) t = log(1.5636) / log(1.0396) t = 0.194 / 0.017 t = 11.41 years
So, the closest answer is 11.51 years.
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