AGBU $3367$

Compound Interest example $-$ Ben and Jerry save for retirement

We talked in class about the power of compounding to increase the FV of a sum. The historical average yield of the US stock market is $12\%($sometimes higher, sometimes a lot lower, but this is the overall average$).$ Two twin brothers, Ben and Jerry, are starting to think toward the future, and put away some money into the stock market for retirement $($use $12\%$ as your compounding rate$).$ Ben starts at age $19,$ and invests $$1000$ a year at the end of each year. He does this for $12$ years until he is $30,$ then stops and puts nothing else in the account, leaving the balance to continue to grow with no new payments.

His brother Jerry sees what Ben is doing, and thinks that is a good idea. He starts at age $31.$ He knows he is behind, so he doubles up and invests $$2000$ a year for the next $35$ years, until he is $65.($see the table below$)$

For each brother, tell me:

$1$B$)$ How much total did Ben invest?

$1$J$)$ How much total did Jerry invest?

$2$B$)$ How much money will Ben have to retire on when he reaches age $65?$

Jerry?

Now redo your calculations, but increase the amount they each put in each year up to the IRA limit$,$ $$\frac{6000}{y}r,$ and use return of only $8\%$ per year. These will be $3B)$ and $3J)$ for total investment, and $4B)$ and $4J)$ for total amount in the IRA at age $65.$

Then write a paragraph or so about what this means to you in your personal finances, and what you should do about it$.$ This will count as two $10-$point homework assignments, $8$ points for your Ben information, and $8$ points for your Jerry information. The paragraph is worth $4$ points total, and will be divided up between the two HW grades to finish out the $10$ point totals for each.

$\backslash$table$[[$Investments$,,],[$YEAR$,$AGE,BEN,JERRY$],[1,19,$$$1000,],[2,20,$$$1000,],[3,21,$$$1000,],[4,22,$$$1000,],[5,23,$$$1000,],[6,24,$$$1000,],[7,25,$$$1000,],[8,26,$$$1000,],[9,27,$$$1000,],[10,28,$$$1000,],[11,29,$$$1000,],[12,30,$$$1000,],[13,31,$No more,$],[14,32,$deposits,$$2000$