Question

Adriana wishes to accumulate $1,980,000 in 35 years. If 35 end-of-year deposits are made into an account that pays interest at a rate of 8% compounded annually, what size deposit is required each year to meet Adriana's stated objective?

Answer 1

Adriana needs to deposit $14,328.07 annually for 35 years at an 8% interest rate to reach her goal of $1,980,000.

Step-by-step explanation:

Adriana can achieve her savings goal by making annual deposits using the formula for the future value of an annuity, which in this case is compounded annually. The formula is given by:

FVA = P × ((1 + r)^n - 1) / r

Where:

Given that Adriana wants to accumulate $1,980,000 over 35 years with an interest rate of 8%, she would need to make an annual payment calculated as follows:

P = FVA / ((1 + r)^n - 1) / r

P = $1,980,000 / (((1 + 0.08)^35 - 1) / 0.08)

The deposit required each year is $14,328.07. Hence, the that Adriana needs to deposit $14,328.07 annually to meet her objective.