$6,055.73
Step-by-step equation:
THE MAIN FORMULA:
initial amount (rate)^the amount of times it is occuring
Step #1, we need to break up the problem for the information:
Tia invests $2,500 at an interest rate of 4%, compounded quarterly,
and another $2,500 at an interest rate of 3.75%, compounded annually. How much are the investments worth at the end of 5 years ?
Step #2, find out how much the first account has in 5 years:
so we know that the rate is 4% quarterly and a quarter is 4. You have to divide 4% (.04 in decimal form) and 4 to get how much the rate is every quarter. That would be .01. After finding how much it is quarterly you would need to add 1. because it is increasing and not decreasing.
For the 20, you would need to multiply 5 and 4. 5 is the amount of years and the 4 is how many times it is happening in that 1 year.
2,500 (1.01)^20
Step #3, find out how much the second account has in 5 years:
we do the exact same steps like we did to find her first account but with different numbers.The number 20 is 5 because it only says for the second account "compounded annually" and annually means oncea year so you would have to mulitiply 5 by 1 and it would get you 5.
To find the rate, we would need to add 1 instead of subtracting one because the problem is and not decreasing. So it would be 3.75% (.0375 in decimal form) plus 1. and it would get you 1.0375.
2,500 (1.0375)^5
The last step is adding the answers to both of those equations together to get the amount of money that she invested:
3005.25 + 3050.48= $6055.73