Jill deposited $2,500 in a savings account at a rate of 7.75%,
compounded monthly. How much was in her account after three months?
You can do this one of two ways.
The long way is to make three problems.
2500 + (2500)x (0.0775/12) = ?? and that will be the amount at the end of the first month.
Then do the problem again for the second month and a third time for th third month.
A shorter way is use the formula for interest compounded.
Amount = 2500*[(0.0775/12)+1.00]3 = ??
I obtained 2548.75 either way.
Assistance needed.
To calculate the amount in Jill's account after three months, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
where:
A = the final amount
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = time in years
In this case, the initial deposit is $2,500, the annual interest rate is 7.75% (0.0775 as a decimal), and interest is compounded monthly (n = 12) for a period of three months (t = 3/12 = 0.25 years).
Let's substitute these values into the formula:
A = 2500(1 + 0.0775/12)^(12*0.25)
Now we can calculate this expression step by step:
1. Calculate the interest rate per compounding period: 0.0775/12 = 0.00646 (rounded to five decimal places).
2. Calculate the exponent in the formula: 12*0.25 = 3.
3. Calculate the value inside parentheses: 1 + 0.00646 = 1.00646 (rounded to five decimal places).
4. Calculate the final amount: 2500 * (1.00646)^3 ≈ 2575.06 (rounded to two decimal places).
Therefore, Jill's account had approximately $2,575.06 after three months.
To calculate the amount in Jill's account after three months, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Amount in the account after specified time
P = Principal amount (initial deposit)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
In this case:
P = $2,500
r = 7.75% = 0.0775 (converted to decimal form)
n = 12 (compounded monthly)
t = 3 months (converted to years by dividing by 12)
Plugging in these values into the formula, we can calculate the amount in Jill's account after three months:
A = 2500(1 + 0.0775/12)^(12*3/12)
A = 2500(1 + 0.006458333)^1
A = 2500(1.006458333)^1
A ≈ $2,530.15
Therefore, after three months, Jill will have approximately $2,530.15 in her savings account.