1)Jennifer invests $800 at 5.75%/a. What is the interest earned in 10 months?
(remember "time" must be converted to years and percent must be converted to decimals)
2) Irina has $3400 in her account, which pays 9% per annum compounded monthly. How much will she have after two years and eight months?
3) Larry’s account pays 4.35% per annum compounded annually. There is $7400 in the account. How much did he invest five years ago?
1) To find the interest earned in 10 months, we need to convert the time to years by dividing by 12:
10 months / 12 = 0.83 years
Next, we need to convert the interest rate to decimal form by dividing by 100: 5.75% / 100 = 0.0575
Now we can calculate the interest earned by multiplying the principal ($800) by the interest rate (0.0575) and the time (0.83 years):
Interest = $800 * 0.0575 * 0.83 = $37.90
Therefore, Jennifer earned $37.90 in interest in 10 months.
2) To calculate the amount Irina will have after two years and eight months, we need to convert the time to years by dividing by 12:
2 years + (8 months / 12) = 2 + (2/3) = 2.67 years
We also need to convert the interest rate to decimal form by dividing by 100: 9% / 100 = 0.09
Now we can use the compound interest formula:
Amount = Principal * (1 + (interest rate / number of compounding periods)) ^ (number of compounding periods * time)
In this case, the principal is $3400, the interest rate is 0.09, the number of compounding periods is 12 (monthly compounding), and the time is 2.67 years.
Amount = $3400 * (1 + (0.09 / 12)) ^ (12 * 2.67)
Amount ≈ $4071.09
Therefore, Irina will have approximately $4071.09 after two years and eight months.
3) To find out how much Larry invested five years ago, we use the compound interest formula to find the principal:
Principal = Amount / (1 + (interest rate / number of compounding periods)) ^ (number of compounding periods * time)
In this case, the amount is $7400, the interest rate is 4.35%, the number of compounding periods is 1 (annual compounding), and the time is 5 years.
Principal = $7400 / (1 + (0.0435 / 1)) ^ (1 * 5)
Principal ≈ $6034.35
Therefore, Larry invested approximately $6034.35 five years ago.
1) To calculate the interest earned, we need to use the formula: Interest = Principal * Rate * Time.
First, we need to convert the time to years. Since interest is calculated in terms of years, 10 months is equivalent to 10/12 = 0.8333 years.
Next, we need to convert the rate to a decimal. 5.75% is equivalent to 5.75/100 = 0.0575.
Now, we can calculate the interest earned:
Interest = $800 * 0.0575 * 0.8333
Interest = $38.33
Therefore, Jennifer will earn $38.33 in interest in 10 months.
2) To calculate how much Irina will have after two years and eight months, we can use the compound interest formula: A = P(1 + r/n)^(nt).
P = Principal amount = $3400
r = Annual interest rate = 9% = 0.09 (as a decimal)
n = Number of times interest is compounded per year = 12 (monthly)
t = Time in years = 2 years + 8 months = 2 + 8/12 = 2.67 years
Now, we can calculate the amount Irina will have:
A = $3400(1 + 0.09/12)^(12 * 2.67)
A = $3400(1.0075)^(32.04)
A ≈ $3939.28
Therefore, Irina will have approximately $3939.28 in her account after two years and eight months.
3) To calculate how much Larry invested five years ago, we can use the compound interest formula in reverse:
P = Principal amount = ?
r = Annual interest rate = 4.35% = 0.0435 (as a decimal)
n = Number of times interest is compounded per year = 1 (annually)
t = Time in years = 5 years
A = Final amount = $7400
Now, we can rearrange the formula to solve for the principal amount (P):
A = P(1 + r/n)^(nt)
P = A / (1 + r/n)^(nt)
P = $7400 / (1 + 0.0435/1)^(1 * 5)
P = $7400 / (1.0435)^5
P ≈ $6369.28
Therefore, Larry invested approximately $6369.28 five years ago.