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Chapter 10: Problem 37

How much should be deposited in an account paying \(7.2 \%\) interest compounded monthly in order to have a balance of \(\$ 15,503.77\) three years from now?

Short Answer

Expert verified
The initial deposit (P) to be made in the account is approximately \$13,137.94

Step by step solution

01

Convert Interest Rate

Convert the interest rate from a percentage to a decimal by dividing by 100. So, \( r = 7.2/100 = 0.072 \)
02

Rearrange the Formula

Since we are trying to find the initial deposit (P), we rearrange the compound interest formula to solve for P: \( P = A / (1 + r/n) ^{nt} \)
03

Substitute Given Values

Substitute the given values into the equation: \( A = \$15,503.77, r = 0.072, n = 12 (since the interest is compounded monthly), t = 3. Subsituting these in gives \( P = \$15,503.77 / (1 + 0.072/12) ^ {12 * 3} \)
04

Calculate

Solve the equation to find P which gives us the amount to be deposited initially.

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