Ryder deposits $500 into an account that earns 4.5% per year. Determine the amount in
the account after 5 years if the interest is:
a) Simple Interest
b) Compounded Monthly
a) 500 + (500 * .045 * 5)
b) 500 * [1 + (.045 / 12)]^60
5 years is 60 monthly compoundings
ty needed this for math class
To determine the amount in the account after a specified period of time with different types of interest, we can use the formulas for simple interest and compound interest.
a) Simple Interest:
Simple interest is calculated by multiplying the principal (initial amount) by the interest rate and the time period. The formula for calculating simple interest is as follows:
Simple Interest = Principal x Interest Rate x Time
In this case, Ryder's initial deposit is $500 and the interest rate is 4.5% per year. The time period is 5 years. Plugging in these values into the formula, we get:
Simple Interest = $500 x 0.045 x 5
= $112.50
To find the amount in the account after 5 years, we need to add the simple interest to the initial deposit:
Amount = Initial Deposit + Simple Interest
= $500 + $112.50
= $612.50
Therefore, the amount in the account after 5 years, with simple interest, is $612.50.
b) Compounded Monthly:
Compound interest is calculated by adding the interest earned on the principal and any previously accumulated interest. The frequency at which the interest is compounded affects the calculation.
The formula for compound interest with monthly compounding is as follows:
Amount = Principal x (1 + (Interest Rate / Number of compounding periods per year))^(Number of compounding periods per year x Time)
In this case, the principal is $500, the interest rate is 4.5% per year, and the compounding is done monthly. The time period is 5 years, which corresponds to 60 months. Plugging in these values into the formula, we get:
Amount = $500 x (1 + (0.045 / 12))^(12 x 5)
= $500 x (1 + 0.00375)^(60)
= $500 x (1.00375)^(60)
≈ $500 x 1.225043
≈ $612.52
Therefore, the amount in the account after 5 years, with monthly compounded interest, is approximately $612.52.