You've mixed up ##p## and ##s##. ##p## is the final value of the investment, and ##s## is the amount initially invested. Make sure you understand what each variable in a formula represents instead of plugging numbers in willy-nilly.lil.l3b91 said:Homework Statement
Michael's investment in his savings account matured to $4,106.32 at the end of 165 days. If the account was earning simple interest at a rate of 4.80% p.a., answer the following.
a. What was Michael's initial investment?
Round to the nearest cent
b. How much interest did Michael earn?
Round to the nearest cent
Homework Equations
p=s(1+rt) ?
I=prt
The Attempt at a Solution
s=4,106.32
t=165/365
r=0.048
s=4,106.32(1+0.048*165/365)
Simple interest is a type of interest that is calculated only on the initial principal amount invested or borrowed. It does not take into account any additional interest earned or charged on that initial amount. It is calculated by multiplying the principal amount, the interest rate, and the number of time periods (usually years) together. For example, if you invest $1,000 in a savings account with a 3% annual interest rate for 5 years, your simple interest would be $150 ($1,000 x 0.03 x 5).
The amount of interest earned on an investment can be calculated by subtracting the initial principal amount from the final amount, in this case $4,106.32. Assuming the initial principal amount was $1,000, the interest earned would be $3,106.32 ($4,106.32 - $1,000).
The length of time it takes for an investment to mature can be calculated by dividing the final amount by the initial principal amount and then dividing by the interest rate. In this case, the final amount is $4,106.32 and the initial principal amount is $1,000. Assuming the interest rate was 3%, it would take approximately 13.69 years for the investment to mature ($4,106.32 / $1,000 / 0.03).
The main difference between simple interest and compound interest is that with compound interest, the interest earned or charged is added to the initial principal amount and then calculated again for the next time period. This means that the interest is compounded over time, resulting in a higher return on investment compared to simple interest. In our example, if the investment had been earning compound interest, the final amount would have been higher than $4,106.32.
To calculate the interest rate, you can divide the interest earned (final amount - initial principal amount) by the initial principal amount and then divide by the number of time periods. In this example, the interest earned was $3,106.32, the initial principal amount was $1,000, and the length of time was 5 years. The interest rate would be 6.21% ($3,106.32 / $1,000 / 5).