Question

I want to have a college fund for my daughter. She is 5, so I have 13 years to achieve my goal of $50,000. The bank says I can earn 2%. I have $5000 already set aside. How much do I need to contribute every year?

Answer 1

You will need to contribute approximately $2,615.97 each year to your college fund to achieve your goal of $50,000 in 13 years, starting with $5,000 and earning 2% interest compounded annually.

Step-by-step explanation:

To calculate how much you need to contribute every year to have $50,000 in a college fund for your daughter in 13 years with an existing $5,000 at a 2% annual interest rate, we need to use the future value of an annuity formula:

The future value of an annuity formula is FV = P × {[(1 + r)^n - 1] / r}, where:

• FV is the future value of the annuity (the amount we want to have in the future, which is $50,000).
• P is the annual payment (the amount you will contribute every year).
• r is the annual interest rate (which is 2%, or 0.02).
• n is the number of years the money is deposited (13 years).

Since you already have $5,000, we first need to find out how much this amount will grow to in 13 years at an annual interest rate of 2%. That's calculated using the compound interest formula:$5,000(1 + 0.02)^{13} = $6,727.09

Now, subtract this future value of your initial savings from the goal:$50,000 - $6,727.09 = $43,272.91

This is the amount that needs to be reached with the annual contributions. Plugging this back into the future value of an annuity formula, we solve for P:$43,272.91 = P × {[(1 + 0.02)^{13} - 1] / 0.02}We can now solve for P, which is the annual contribution required:P = $43,272.91 / {[(1 + 0.02)^{13} - 1] / 0.02} = $2,615.97

Therefore, you'd need to contribute approximately $2,615.97 each year to reach your $50,000 college fund goal in 13 years, assuming a 2% annual rate.

Answer 2

$2960 yearly savings

Step-by-step explanation:

From the values given and from mathematical manipulation, he or she needs a contribution of at least $2900 every year in order to achieve his goal of $50,000.

EXPLANATION

• If the child is 5yr old now, in 13years time, she will be 18yr old.

• $2950 target yearly

• for the next 13years, it would have amount to $38350

• remember the bank will give an annual interest rate of 2%

• so for 13years, that's 26% = 0.26

• In the 13th year, he would have saved $38350, add the 26% interest for the duration of 13years = 26% x $38350 + $38350 = $48321

• His savings will fall between $2950 - $2960 yearly.