Question

Account balance of 1723.57 the interest rate of the account is 3.4% compounded daily. If the account was opened 9 years ago, what was the value of the initial deposit

Answer 1

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:

$P = A(1 + \frac{r}{n} )^{-nt}$

Here,

A = 1723.57

r = 3.4% = 0.034

n = 365 (because it is compounded daily )

t = 9

So,

we get

$P = 1723.57(1 + \frac{0.034}{365} )^{-365(9)}$

   = 1723.57(1.000093151)⁻³²⁸⁵

   = 1723.57(0.736396351)

   = 1269.23066 ≈ $1269

∴ we get

The value of the initial deposit = $1269