Question

Juan has a goal of saving up $57,865 by making biweekly (26 per year) deposits into a savings account for the next 5 years. If the account has an annual interest rate of 1%, how much should each of his deposits be?

Answer 1

Explanation:

To calculate the amount of each biweekly deposit that Juan should make to save up $57,865 in 5 years with an annual interest rate of 1%, we can use the formula for the future value of an ordinary annuity.

The formula for the future value of an ordinary annuity is:

FV = P * [(1 + r)^n - 1] / r

Where:

FV = Future value of the annuity

P = Amount of each deposit

r = Interest rate per period

n = Number of periods

In this case, the future value (FV) is $57,865, the interest rate (r) is 1% per year, and the number of periods (n) is 26 deposits per year multiplied by 5 years, which is 130.

Let's calculate the amount of each deposit (P):

57,865 = P * [(1 + 0.01)^130 - 1] / 0.01

Simplifying the equation, we have:

57,865 = P * [1.01^130 - 1] / 0.01

To solve for P, we divide both sides of the equation by [1.01^130 - 1] / 0.01:

P = 57,865 / [1.01^130 - 1] / 0.01

Using a calculator to evaluate the expression, we find:

P ≈ $222.71

Therefore, Juan should make biweekly deposits of approximately $222.71 to save up $57,865 in 5 years with an annual interest rate of 1%.