Annuities and Loans

Question

Hello! I have been stuck on this math problem all day! I hope someone can help me.

you want to be able to withdraw 30,000 each year for 20 years. Your account earns 7% interest. How much do you need in your account at the beginning?

thank you!

Answer 1

Actually, what you have here is an annuity problem. For this scenario, we can’t use a basic interest formula, we need to use a sum of a geometric series. Assuming payments are made at the start of each year, our formula will be:

future value = starting value x rate ^ (periods-1) - withdrawl amount x ((rate ^ periods) - 1)/(rate - 1)

Future value can can be set to 0 (we are just funding the 20 $30,000 payments).

The start value is what we’re solving for in this case.

Rate is 1.07 (the seven percent interest each year).

Withdrawl amount is $30,000.

Solving for the start value value gives an answer of $340,067.86 for an initial investment.

I hope this explanation helps! Please give it an upvote if you found it helpful, or comment if you have any other questions. Thanks!

Answer 2

Carly,

At some point in the future you need to have 30,000*20 =600,000$ the reason you are probably having trouble is the is no single answer

We know that A0*(1.07)ⁿ=600,000 where A0 in the initial amount and n is the number of years A0 is invested.

For example if you had $305,000 to invest for 10 years you would have the $600,000 you need.

Basically you have one equation an 2 unknowns

Hope this helps

Jim