Question

Determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate. You will need to determine the value for r to solve this problem. When finding r round it to the nearest ten thousandths. Deposit amount: $50; total deposits: 60; interest rate: 5%, compounded monthly The value for r is Answer The value of the annuity is $Answer

Answer 1

$3,408.49

Explanation:

To determine the value of the annuity, we need to use the formula for the future value of an ordinary annuity:

A = P * ((1 + r)^n - 1) / r

Where:

A = Value of the annuity

P = Monthly deposit amount

r = Interest rate per period (monthly interest rate in this case)

n = Total number of deposits

First, let's convert the annual interest rate of 5% to a monthly interest rate. We divide the annual interest rate by 12 (number of months in a year) and convert it to a decimal:

Monthly interest rate = 5% / 12 = 0.05 / 12 = 0.0041667

Next, let's substitute the given values into the annuity formula:

P = $50

r = 0.0041667 (monthly interest rate)

n = 60

A = $50 * ((1 + 0.0041667)^60 - 1) / 0.0041667

Now we can calculate the value of the annuity using a calculator or spreadsheet:

A ≈ $50 * (1.0041667^60 - 1) / 0.0041667 ≈ $50 * (1.28370557 - 1) / 0.0041667 ≈ $50 * 0.28370557 / 0.0041667 ≈ $50 * 68.169768 ≈ $3,408.49