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Chapter 3: Problem 23

Suppose a bank account paying \(4 \%\) interest per year, compounded 12 times per year, contains \(\$ 10,555\) at the end of 10 years. What was the initial amount deposited in the bank account?

Short Answer

Expert verified
The initial amount deposited in the bank account was approximately $7,978.30.

Step by step solution

01

Identify the given values

We are given the following: - final amount A: $10,555 - interest rate r: 4% (0.04) - compounding frequency n: 12 times per year - years t: 10 years
02

Rearrange the formula to find P

We need to find the initial amount P. First, let's rearrange the compound interest formula to solve for P: \(P = \frac{A}{(1 + \frac{r}{n})^{nt}}\)
03

Substitute the given values into the rearranged formula

Next, substitute the given values into the rearranged formula: \(P = \frac{10,555}{(1 + \frac{0.04}{12})^{12*10}}\)
04

Simplify and solve for P

Now, we just need to simplify the expression and solve for P: \(P = \frac{10,555}{(1 + 0.003333)^{120}}\) \(P = \frac{10,555}{1.003333^{120}}\) \(P 鈮� 7,978.30\)
05

Interpret the result

The initial amount deposited in the bank account was approximately $7978.30.

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