Answer:
The value of the initial deposit = $1269
Explanation:
Given - Account balance of 1723.57 the interest rate of the account is 3.4% compounded daily.
To find - If the account was opened 9 years ago, what was the value of the initial deposit
Proof -
We know that,
If the interest rate is compounded n times per year at an annual rate r, the present value of a A dollars payable t years from now is:
[tex]P = A(1 + \frac{r}{n} )^{-nt}[/tex]
Here,
A = 1723.57
r = 3.4% = 0.034
n = 365 (because it is compounded daily )
t = 9
So,
we get
[tex]P = 1723.57(1 + \frac{0.034}{365} )^{-365(9)}[/tex]
= 1723.57(1.000093151)⁻³²⁸⁵
= 1723.57(0.736396351)
= 1269.23066 ≈ $1269
∴ we get
The value of the initial deposit = $1269
