Answer:
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
In which I is the amount earned with interest, P is the money deposited(the principal), t is the time in years and r is the annual interest rate, as a decimal.
At the end of the period, the total amount is:
Joe deposits 10 today and another 30 in five years into a fund paying simple interest of 11% per year.
So, he is going to have two interests.
For the first one: He deposits 10, so . The period is 10 years, so . The annual rate is 11%, so
His first interest is:
From the first interest, Joe's amount is
The second one: He deposits 30, so . The period goes from the 5th to the 10th years, so . The annual rate is 11%, so .
His second interest is:
From the second interest, his amount is:
Joe's total amount is:
Now for Tina
Tina will make the same two deposits, but the 10 will be deposited n years from today and the 30 will be deposited 2n years from today. Tina’s deposits earn an annual effective rate of 9.15%. At the end of 10 years, the accumulated amount of Tina’s deposits equals the accumulated amount of Joe’s deposits.
Tina has two deposits, each one with an amount, for the first deposit and for the second deposit. Her accumulated amount is equal to Joe's. Joe is 67.5. So:
is the principal of 10 plus the interest. So
is the principal of 30 plus the interest. So
is the interest earned from her deposit of 10. This means that . The interest rate is 9.15%. So . The deposit will happen n years from today and will end in 10 years. So . So
is the interest earned from her deposit of 30. This means that . The interest rate is 9.15%. So . The deposit will happen 2n years from today and will end in 10 years. So . So
We have that:
*(-1)