Skills Quiz - FinanceScore: 0/400/10 answered(1)1hr27 minsxProgress savedSubmit and EndQuestion 14 ptsYou deposit $4000 in an account earning 5% interest compounded monthly. How much will you have in the account in 10 years?$Check Answer58∘FMostly sunnySearch
Q. Skills Quiz - FinanceScore: 0/400/10 answered(1)1hr27 minsxProgress savedSubmit and EndQuestion 14 ptsYou deposit $4000 in an account earning 5% interest compounded monthly. How much will you have in the account in 10 years?$Check Answer58∘FMostly sunnySearch
Identify Variables: First, identify the variables needed to calculate the future value of the investment:Principal amount P = $4000Annual interest rate r = 5% or 0.05Number of times the interest is compounded per year n = 12 (monthly)Number of years t = 10
Convert to Monthly Rate: Convert the annual interest rate to a monthly interest rate by dividing by the number of times interest is compounded per year:Monthly interest rate r/n = 0.05/12
Use Compound Interest Formula: Use the formula for compound interest to calculate the future value ( extit{A}): extit{A} = extit{P}(1 + extit{r}/ extit{n})^{( extit{nt})}
Substitute Values: Substitute the values into the formula:A=4000(1+0.0041666667)(12×10)
Calculate Exponent: Calculate the exponent part of the formula: nt=12×10=120
Calculate Future Value: Calculate the future value using the formula with all values substituted:A=4000(1+0.0041666667)120
Perform Calculation: Perform the calculation:A≈4000(1.0041666667)120A≈4000×1.647009A≈6588.036