Question

Please show work for all parts, thank you :)

(Comprehensive problem) You would like to have $ 78,000 in 12 years. To accumulate this amount, you plan to deposit an equal sum in the bank each year that will earn 7 percent interest compound

Answer 1

To accumulate $78,000 in 12 years by making equal annual deposits, we can use the future value of an ordinary annuity formula.

Given data:

Target amount (Future value) = $78,000

Number of years = 12

Interest rate = 7% (compounded annually)

Let's denote the equal annual deposit as X.

Using the future value of an ordinary annuity formula:

Future Value = X * [(1 + Interest rate)^Number of years - 1] / Interest rate

Plugging in the values:

$78,000 = X * [(1 + 0.07)^12 - 1] / 0.07

Let's solve for X:

$78,000 * 0.07 = X * [(1.07)^12 - 1]

$5,460 = X * (1.07^12 - 1)

$5,460 = X * 1.967151

X = $5,460 / 1.967151

X = $2,779.06

Therefore, you would need to deposit approximately $2,779.06 each year for 12 years to accumulate $78,000, assuming a 7% interest rate compounded annually.