find (a) the future value of the given principal p and (b) the interest earned in the given period. p =…

find (a) the future value of the given principal p and (b) the interest earned in the given period. p = $3200 at 6.5% compounded annually for 18 years. (a) the future value of the principal after 18 years is $ (round to the nearest cent as needed.)

find (a) the future value of the given principal p and (b) the interest earned in the given period. p = $3200 at 6.5% compounded annually for 18 years. (a) the future value of the principal after 18 years is $ (round to the nearest cent as needed.)

Answer

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula for annual compounding is $A = P(1 + r)^t$, where $A$ is the future value, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. Given $P=$3200$, $r = 0.065$ (since $6.5%=0.065$), and $t = 18$.

Step2: Substitute values into the formula

$A=3200\times(1 + 0.065)^{18}$ First, calculate $(1 + 0.065)^{18}$. $(1 + 0.065)^{18}=1.065^{18}\approx3.077247$. Then, $A = 3200\times3.077247\approx9847.19$.

Step3: Calculate the interest earned

The interest earned $I=A - P$. $I=9847.19 - 3200=$6647.19$

Answer:

(a) $$9847.19$ (b) $$6647.19$