Question

If you want to save $40,100 for a down payment on a home in five years, assuming an interest rate of 4.5 percent compounded annually, how much money do you need to save at the end of each month?

a.

$597.21

b.

$616.54

c.

$628.51

d.

$598.58

Answer 1

To save $40,100 for a down payment in five years with an interest rate of 4.5% compounded annually, you need to save approximately $597.21 at the end of each month.

Step-by-step explanation:

To calculate the amount of money needed to save at the end of each month, we can use the formula for future value of an ordinary annuity:

FV = PMT x ((1 + r)^n - 1) / r

Where:

1. FV is the future value or the total amount needed to save ($40,100)
2. PMT is the monthly savings amount that we need to find
3. r is the interest rate per period (4.5% compounded annually divided by 12)
4. n is the number of periods (5 years multiplied by 12 months)

Plugging in the values, we get:

FV = PMT x ((1 + (0.045/12))^(5*12) - 1) / (0.045/12)

Simplifying the equation:

40,100 = PMT x (1.00375^60 - 1) / (0.00375)

PMT = 40,100 x (0.00375) / (1.00375^60 - 1)

PMT ≈ $597.21

Answer 2

The correct answer is $598.58. This means that in order to save $40,100 for a down payment on a home in five years, with an annual interest rate of 4.5% compounded annually, you need to save approximately $598.58 at the end of each month. This monthly savings amount takes into account the interest earned on your savings over the five-year period. By consistently saving this amount each month, you will reach your goal of $40,100 within the specified timeframe.