Question

Sally wants to save up for new furniture. She wants to have $2,600 to purchase the furniture in 34 months. If she opens a savings account that pays 1.84% annual interest compounded monthly, how much will she need to deposit to reach her goal?

Answer 1

To calculate the amount Sally needs to deposit, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the initial deposit, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Step-by-step explanation:

To calculate the amount Sally needs to deposit, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the initial deposit, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, P is the unknown we want to solve for, A is $2,600, r is 1.84% or 0.0184, n is 12 (since interest is compounded monthly), and t is 34 months divided by 12 to convert it to years.

Substituting the values into the formula, we have:

A = P(1 + r/n)^(nt)

$2,600 = P(1 + 0.0184/12)^(12(34/12))

Simplifying the equation, we can solve for P by dividing both sides of the equation by (1 + 0.0184/12)^(12(34/12)). This will give us the value of P, which is the amount Sally needs to deposit.