the following money market account rates were available from a particular bank. find the compound amount and…

the following money market account rates were available from a particular bank. find the compound amount and the interest earned.\n$17,000 at 0.87% compounded monthly for three years\n\nthe compound amount is $□.\n(do not round until the final answer. then round to the nearest cent as needed.)

the following money market account rates were available from a particular bank. find the compound amount and the interest earned.\n$17,000 at 0.87% compounded monthly for three years\n\nthe compound amount is $□.\n(do not round until the final answer. then round to the nearest cent as needed.)

Answer

Explanation:

Step1: Define compound interest formula

The formula for compound amount is $A = P\left(1+\frac{r}{n}\right)^{nt}$, where:

  • $P$ = principal amount, $r$ = annual interest rate (decimal), $n$ = number of times compounded per year, $t$ = time in years.

Step2: Convert rate to decimal

$r = \frac{0.87}{100} = 0.0087$

Step3: Identify all values

$P = 17000$, $n = 12$, $t = 3$, $r = 0.0087$

Step4: Calculate monthly rate + 1

$\frac{r}{n} + 1 = 1+\frac{0.0087}{12} = 1 + 0.000725 = 1.000725$

Step5: Calculate total compound periods

$nt = 12\times3 = 36$

Step6: Compute compound amount

$A = 17000\times(1.000725)^{36}$ First calculate $(1.000725)^{36} \approx 1.026417$ Then $A = 17000\times1.026417 \approx 17449.09$

Answer:

The compound amount is $$17449.09$ The interest earned is $$17449.09 - $17000 = $449.09$