Question

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?

Answer 1

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.