Answer:
You have to deposit $8,207.5 today.
Step-by-step explanation:
Compound interest:
The amount of money in yearly compounded interest, after t years, is given by the following equation:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which A(0) is the initial deposit and r is the interest rate, as a decimal.
You would like to have $10,000 in an account after eight years time.
This means that when [tex]t = 8, A(t) = 10000[/tex]
2.5% compounded interest
This means that [tex]r = 0.025[/tex]
So
[tex]A(t) = A(0)(1+r)^t[/tex]
[tex]A(t) = A(0)(1+0.025)^t[/tex]
[tex]A(t) = A(0)(1.025)^t[/tex]
How much would you have to deposit today?
We have to find A(0), when [tex]t = 8, A(t) = 10000[/tex]. So
[tex]A(t) = A(0)(1.025)^t[/tex]
[tex]10000 = A(0)(1.025)^8[/tex]
[tex]A(0) = \frac{10000}{(1.025)^8}[/tex]
[tex]A(0) = 8207.5[/tex]
You have to deposit $8,207.5 today.
