Respuesta :
Answer:
difference = $12093.38
Explanation:
given data
adds 1st day in saving account = $1,500
adds last day in saving account = $1,500
annual interest = 6.5 %
time = 35 year
to find out
difference in their savings account balances
solution
we get there first Theresa future value that is
future value 1 = present value × [tex]\frac{(1+rate)^{time} - 1}{rate}[/tex] ....1
future value 1 = $1500 × [tex]\frac{(1+0.065)^{35} - 1}{0.065}[/tex]
future value 1 = $186052.04
and
future value 2 = present value × [tex]\frac{(1+rate)^{time} - 1}{rate}[/tex] × (1+rate) .........2
future value 2 = $1500 × [tex]\frac{(1+0.065)^{35} - 1}{0.065}[/tex] × (1+0.065)
future value 2 = $198145.42
so that here difference is
Difference = $198145.42 - $186052.04
difference = $12093.38
The difference in Theresa and marcus savings account at the end of 35 years will be $12,092.84
What is Future Value of cash flows?
The future value of one cash flow is its value after accumulating interest a few times. The future value of a cash flow equals the sum of the future value of each cash flow.
As per the given information,
First day in saving account is equal to $1,500
Last day in saving account is equal to $1,500
annual interest is 6.5 %
time is 35 years
Difference in their savings account balances:
We get there first Theresa future value that is:
[tex]\rm\,FV = Present\, Value [\dfrac{(1+r)^{n}- 1 } {r}]\\\rm\,FV = 1,500 [\dfrac{9.0623- 1} {0.065}]\\\\\rm\,FV = 1,500\times 124.035\\\\rm\,FV = $186,053.07[/tex]
In case of Marcus, where the payment is made at the end of the year:
[tex]\rm\,FV = Present\,Value[\dfrac{(1+r)^{n}-1 } {r}](1 + r)\\\\FV= 1,500[\dfrac{(1+0.065)^{35} -1} {0.065}](1 + 0.065)\\\\FV = 1,500[\dfrac{(9.0623 -1)} {0.065}](1 + 0.065)\\\\FV = 1,500 \times\,124.035(1 + 0.065)\\\\\FV = 1,500\times 132.097\\\\FV = $198,145.913[/tex]
[tex]\rm\,Difference\, Between \, Their \, Furture\, Values = \rm\,\$198,145.91 - \$186,053.07\\\ \\\rm\,Difference= \$ 12,092.84[/tex]
Thus, the difference between their future values at the end of 35 years is equal to $12,092.84
To learn more about Future Value of Cash flows, refer to the
https://brainly.com/question/26371663
