Question

Assume that, starting next year, you make annual deposits of $205 into a savings account that pays 4% interest. How much will you have in your account after 3 years? Enter your answer in terms of dollars and cents, rounded to 2 decimals, and without the dollar sign. That means, for example, that if your answer is $127.5678, you must enter 127.57

Answer 1

After making annual deposits of $205 for 3 years in a savings account with a 4% interest rate, the account would have $630.81.

Step-by-step explanation:

Assuming that you make annual deposits of $205 into a savings account that pays a 4% interest rate, to calculate the total amount in the account after 3 years, we need to apply the formula for the future value of a series of equal payments (ordinary annuity).

The formula is given by: FV = P × ((1 + r)^n - 1) / r, where P is the payment amount, r is the interest rate per period, and n is the number of periods.

Here, P = $205, r = 4% or 0.04, and n = 3 years. Using the formula, the future value FV is:

FV = 205 × ((1 + 0.04)^3 - 1) / 0.04

FV = 205 × ((1.04^3 - 1) / 0.04)

Calculating this gives us a future value of approximately 630.81, which when rounded to two decimals is 630.81.

Therefore, after 3 years, the account will have $630.81.