Question - Compound Interest Calculation with Monthly Compounding
Solution:
To solve for the amount Jace will have in the account after one year with an annual percentage rate of 3.8% and monthly compounding interest, we use the formula for compound interest: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.- t is the time the money is invested for, in years.Given:P = $2,000r = 3.8% or 0.038 (as a decimal)n = 12 (since interest is compounded monthly)t = 1 yearPlugging these into the formula gives us:A = 2000(1 + 0.038/12)^(12*1)A = 2000(1 + 0.0031667)^(12)A = 2000(1.0031667)^(12)Calculating this out, we get:A ≈ 2000(1.038565)A ≈ 2077.13So, after rounding to the nearest penny, Jace will have approximately $2077.13 in the account after one year.The question also asks for the annual percentage yield (APY). The APY takes into account the effect of monthly compounding and is calculated using the formula:APY = (1 + r/n)^(n) - 1Using the same values for r and n:APY = (1 + 0.038/12)^(12) - 1APY = (1.0031667)^(12) - 1APY ≈ 0.038818 or 3.8818%After converting this to a percentage and rounding to the nearest hundredth of a percent, the APY is approximately 3.88%.
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