Zeb is going to deposit $3370 into an account that earns 14% APR compounded annually for 37 weeks.
What is the "n" in the compound interest formula?
n=
What is the "t" in the compound interest formula? Enter as a fraction.
years
What is the "nt" in the compound interest formula? Enter as a fraction
nt=
How much money will Zeb have in this account 37 weeks from now?
$
How much of this amount is from interest earned?
it will never compound if it is compounded annually for 37 weeks because 37 weeks is less than a year
okay so what do i do?
To find the values of "n," "t," and "nt" in the compound interest formula, we need to convert 37 weeks to a fraction of a year.
1. "n" in the compound interest formula represents the number of compounding periods per year. In this case, the interest is compounded annually, so "n" is equal to 1.
2. "t" in the compound interest formula represents the time in years. You mentioned that 37 weeks is the time period, so we need to convert it to years. There are 52 weeks in a year, so we can divide 37 by 52 to get the fraction of a year. Therefore, "t" is equal to 37/52.
3. "nt" in the compound interest formula is the product of "n" and "t." We can calculate this by multiplying 1 (the value of "n") with 37/52 (the value of "t"). The result is equal to 37/52.
Now, to calculate the final amount, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A is the final amount (the amount Zeb will have in the account)
P is the principal amount (the initial deposit)
r is the annual interest rate (in decimal form)
n is the number of compounding periods per year
t is the time in years
In this case, the principal amount (P) is $3370, the annual interest rate (r) is 14% (or 0.14 in decimal form), and we already found the values of "n" and "t."
Now we can plug in these values into the formula to find the final amount:
A = $3370(1 + 0.14/1)^(1 * 37/52)
Calculating this, we find that Zeb will have approximately $3,870.42 in the account after 37 weeks.
To find the amount of money that is from interest earned, we can subtract the initial deposit from the final amount:
Interest earned = $3,870.42 - $3370 = $500.42
Therefore, approximately $500.42 of the final amount is from interest earned.