Mike's grandmother opened a savings account in Mike's name and deposited some money into the account. The account pays an annual simple interest rate of 11%. After 13 years, the interest earned on the account is $5720. How much money did Mike's grandmother deposit into the account?
I = PRT
5720 = P * 0.11 * 13
5720 = 1.43P
4,000 = P
Mike's grandmother opened a savings account in Mike's name and deposited some money into the account. The account pays an annual simple interest rate of 4%. After 13 years, the interest earned on the account was $2,080. How much money did Mike's grandmother deposit in the account?
To calculate the amount deposited into Mike's account, we can use the formula for simple interest:
Interest = Principal * Rate * Time
We are given the following information:
- Interest earned = $5720
- Rate = 11% (0.11 in decimal form)
- Time = 13 years
Let's substitute these values into the formula and solve for the principal (amount deposited):
$5720 = Principal * 0.11 * 13
Dividing both sides of the equation by (0.11 * 13):
$5720 / (0.11 * 13) = Principal
Principal = $4000
Therefore, Mike's grandmother deposited $4000 into his savings account.
To find the amount deposited by Mike's grandmother, we can use the formula for simple interest:
I = P * r * t,
where:
I = interest earned,
P = principal amount (the amount deposited),
r = interest rate per period, and
t = number of periods.
In this case, we are given:
I = $5720,
r = 11% = 0.11 (converted to decimal),
and t = 13 years.
We need to solve for P, so we can rearrange the formula as:
P = I / (r * t).
Substituting the given values, we have:
P = 5720 / (0.11 * 13).
Calculating this, we get:
P ≈ $4,000.
Therefore, Mike's grandmother deposited approximately $4,000 into the savings account.