It is given that the amount invested is $3000 with an interest rate of 4.1% compounded monthly.
It is required to find the amount in 1 year and the annual percentage yield.
The formula for Compound Interest is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where:
• A= final amount
,
• P= amount invested initially
,
• r= interest rate
,
• n= number of times interest is compounded in a year
,
• t= number of years
Substitute P=3000, r=4.1%=0.041, n=12 (compounded monthly), and t=1 into the formula:
[tex]A=3000(1+\frac{0.041}{12})^{12(1)}\approx\$3125.34[/tex]
The formula for the Annual Percentage Yield is given as:
[tex]APY=(1+\frac{r}{n})^n-1[/tex]
Substitute r=0.041, n=12 into the formula:
[tex]APY=(1+\frac{0.041}{12})^{12}-1\approx0.0418=4.18\%[/tex]
Answers:
Amount = $3125.34
APY = 4.18%
