Savannah invested $5,300 in an account paying an interest rate of 3, start fraction, 5, divided by, 8, end fraction3 85 % compounded daily. Zendaya invested $5,300 in an account paying an interest rate of 3, start fraction, 3, divided by, 8, end fraction3 83 % compounded quarterly. After 15 years, how much more money would Savannah have in her account than Zendaya, to the nearest dollar?
Question
Savannah invested 5,300 in an account paying an interest rate of 3, start fraction, 3, divided by, 8, end fraction3 83 % compounded quarterly. After 15 years, how much more money would Savannah have in her account than Zendaya, to the nearest dollar?
Solution
The problem involves comparing the future value of two investments with different compounding periods and interest rates.
First, let's convert the interest rates from fractions to decimals.
For Savannah, the interest rate is 3 5/8 %, which is equivalent to 0.03625 in decimal form.
For Zendaya, the interest rate is 3 3/8 %, which is equivalent to 0.03375 in decimal form.
Next, we'll use the formula for compound interest, which is A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal form).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
For Savannah, who has her interest compounded daily (n = 365), the equation becomes:
A_Savannah = 5300 * (1 + 0.03625/365)^(365*15)
For Zendaya, who has her interest compounded quarterly (n = 4), the equation becomes:
A_Zendaya = 5300 * (1 + 0.03375/4)^(4*15)
To find out how much more money Savannah would have, subtract the amount Zendaya would have from the amount Savannah would have:
Difference = A_Savannah - A_Zendaya
Finally, round the result to the nearest dollar.
Please note that you'll need a calculator to compute these values.
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