Suppose that
$2000 is invested at a rate of
5.1% , compounded semiannually. Assuming that no withdrawals are made, find the total amount after 7 years.
Compound Interest
compounded semiannually
A = P(1+(r/2))^2n
r is annual rate as a decimal
P is principle
n is number of years
A is present value
A = 2000(1.0245)^16 = 2945.92
P = Po(1+r)^n.
Po = $2000.
r = 0.051/2 = 0.0255 = Semi-annual % rate expressed as a decimal.
n = 2Comp./yr. * 7yrs. = 14 Compounding
periods.
Suppose that
$2000
is loaned at a rate of
15%
, compounded monthly. Assuming that no payments are made, find the amount owed after
6
years
To find the total amount after 7 years, we can use the formula for compound interest:
\[A = P \left(1 + \frac{r}{n}\right)^{nt}\]
Where:
A = the total amount after the specified time period
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $2000, the annual interest rate (r) is 5.1% or 0.051, the interest is compounded semiannually (n = 2), and the time period (t) is 7 years.
Substituting the values into the formula:
\[A = 2000 \left(1 + \frac{0.051}{2}\right)^{(2)(7)}\]
Now we can simplify and calculate the answer.