Question

(Compound annuity) You plan on buying some property in Florida 4 years from today. To do this you estimate that you will need $30,000 at that time for the purchase. You would like to accumulate these funds by making equal annual deposits in your savings account, which pays 13 percent annually If you make your first deposit at the end of this year, and you would like your account to reach $30,000 when the final deposit is made, what will be the amount of your deposits? The amount of your end-of year deposits will be $(Round to the nearest cent

Answer 1

To accumulate $30,000 in four years with an interest rate of 13%, one must make annual deposits of approximately $3,174.61.

Step-by-step explanation:

To calculate the amount of equal annual deposits needed to accumulate $30,000 in 4 years with an annual interest rate of 13%, we can use the formula for the future value of an ordinary annuity. The formula is FV = Pmt * (((1 + r)^n - 1) / r), where FV is the future value of the annuity, Pmt is the payment per period, r is the interest rate per period, and n is the number of periods.

Here's the breakdown of the variables:

• FV (Future Value): $30,000
• r (Interest Rate): 13% or 0.13 annually
• n (Number of Deposits): 4

We need to rearrange the formula to solve for Pmt:

Pmt = FV / (((1 + r)^n - 1) / r)

Plugging in the values:

Pmt = $30,000 / (((1 + 0.13)^4 - 1) / 0.13)

Pmt = $30,000 / ((1.13^4 - 1) / 0.13)

Pmt = $30,000 / ((2.229 - 1) / 0.13)

Pmt = $30,000 / (1.229 / 0.13)

Pmt = $30,000 / 9.4538

Pmt ≈ $3,174.61

Therefore, the amount of the end-of-year deposits needed to accumulate $30,000 at an annual interest rate of 13% over 4 years is approximately $3,174.61 when rounded to the nearest cent.