an initial investment amount p, an annual interest rate r, and a time t are given. find the future value of…
an initial investment amount p, an annual interest rate r, and a time t are given. find the future value of the investment when interest is compounded (a) annually, (b) monthly, (c) daily, and (d) continuously. then find (e) the doubling time t for the given interest rate. p = $6500, r = 3.45%, t = 6 yr. a) the future value of the investment when interest is compounded annually is $. (type an integer or a decimal. round to the nearest cent as needed.)
Answer
Explanation:
Step1: Recall compound - interest formula
The compound - interest formula when compounded annually is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. Given $P=$6500$, $r = 0.0345$ (since $3.45%=0.0345$), and $t = 6$.
Step2: Substitute values into formula
$A=6500\times(1 + 0.0345)^6$. First, calculate $(1 + 0.0345)^6$. $(1 + 0.0345)^6=1.0345^6$. Using a calculator, $1.0345^6\approx1.23177$. Then, $A = 6500\times1.23177$. $A\approx7906.505$.
Step3: Round to the nearest cent
Rounding $7906.505$ to the nearest cent gives $A\approx$7906.51$.
Answer:
$7906.51$