Question

Marissa wants to accumulate at least $65,000 by depositing $1,300 at the end of every month into a fund that earns interest at 4.50% compounded monthly.

a. How many deposits does she need to make to reach her goal? (Round to the next payment)
b. How long will it take Marissa to reach her goal? (Express the answer in years and months, rounded to the next payment period)

Answer 1

Marissa needs to make approximately 49 deposits to reach her goal of $65,000 and it will take her approximately 3 years and 7 months.

Step-by-step explanation:

To calculate the number of deposits Marissa needs to make to reach her goal, we can use the formula for the future value of an ordinary annuity:

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

Where FV is the future value, P is the periodic payment, r is the interest rate per period, and n is the number of periods.

Plugging in the given values, we have:

FV = $65,000, P = $1,300, r = 4.50%/12 = 0.375%, n = ?

Solving for n, we get:

n ≈ log((r*FV + P)/(r*P + P))/log(1+r)

Using a financial calculator or spreadsheet software, we find that Marissa needs to make approximately 49 deposits to reach her goal.

To calculate the time it will take Marissa to reach her goal, we can rearrange the formula:

n = log((r*FV + P)/(r*P + P))/log(1+r)

Plugging in the given values, we get:

n = log((0.00375 * $65,000 + $1,300)/(0.00375 * $1,300 + $1,300))/log(1+0.00375)

Using a financial calculator or spreadsheet software, we find that it will take Marissa approximately 3 years and 7 months to reach her goal.