Problem

Hayley invested $\$ 19,000.00$ into an account paying a ridiculous $8 \%$ compounded quarterly. How much money will be in the account after 54 months? Round your final answer to the nearest cent.

Solution

Step 1 :Translate the problem into the formula for future value (FV) of an investment, which is \(FV = P * (1 + r/n)^{nt}\), where P is the principal amount, r is the annual interest rate in decimal form, n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

Step 2 :Given that P = $19,000, r = 8% or 0.08, n = 4 (since interest is compounded quarterly), and t = 54 months or 4.5 years, substitute these values into the formula.

Step 3 :Calculate the future value (FV) using the formula \(FV = 19000 * (1 + 0.08/4)^{4*4.5}\).

Step 4 :Compute the result to get the future value of the investment, which is approximately $27136.68.

Step 5 :\(\boxed{27136.68}\) is the amount of money that will be in the account after 54 months.

From Solvely APP
Source: https://solvelyapp.com/problems/43701/

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