Suppose that $6,500 is placed in an account that pays 11% interest compounded each year assume that no withdrawals are made from the account find the amount and the account at the end of one year
The formula to calculate compound interest is
A = P(1 + r/n)^(nt)
where:
A = the amount of money accumulated after n years, including interest.
P = principal amount (the initial amount of money)
r = annual interest rate (in decimal)
n = number of times that interest applied per time period
t = time the money is invested for, in years
Since the interest is compounded once a year, n=1 and t= 1. r= 11% = 0.11 and P=$6500.
Plugging these into the formula, we get:
A = 6500(1 + 0.11/1)^(1*1)
A = $7215
So, the amount in the account at the end of one year would be $7215.
To find the amount in the account at the end of one year, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, we have:
P = $6,500
r = 11% = 0.11 (decimal)
n = 1 (interest compounded once per year)
t = 1 year
Substituting the given values into the formula, we get:
A = 6500(1 + 0.11/1)^(1*1)
A = 6500(1 + 0.11)^1
A = 6500(1.11)
A = $7,215
Therefore, the amount in the account at the end of one year is $7,215.