Compound Interest Calculation with Monthly Compounding
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 = $2,000
r = 3.8% or 0.038 (as a decimal)
n = 12 (since interest is compounded monthly)
t = 1 year
Plugging 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 ≈ 2077.13
So, 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) - 1
Using the same values for r and n:
APY = (1 + 0.038/12)^(12) - 1
APY = (1.0031667)^(12) - 1
APY ≈ 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%.
