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## Who Will Have More?

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**THE SCENARIO**
This week something reminded me of a classic question that was covered in the first class that taught me how to use a financial calculator. You may not have seen it, though, so today we'll work through it.
Say there are two recent college grads, Angela and Bill. They both make $50,000 per year, and they both want to retire in 40 years. They will both invest their retirement savings in an investment that will yield 8.5% interest per year.
Angela invests 12% of her income for the first 10 years, then stops and lets it grow for the next 30 years.
Bill waits 10 years and then invests 12% of his income for the remaining 30 years.
**The question:** Who has more money after 40 years, and how much more do they have? Assume their income never goes up over time.

**THE SOLUTION**
This one is pretty straightforward, but it has 4 parts.
**Step 1: How much does Angela have after 10 years?**
N: 120 (Angela invests every month for 10 years, which is 10 x 12 = 120 months)
I/YR: 8.5 (The investment yields 8.5% per year)
PV: 0 (Angela starts with nothing)
PMT: -500 (Angela invests $500 per month)
FV: (This is what I'm trying to find)
**Step 2: How much does Angela have at the end?**
N: 360 (Angela retires 30 years later, which is 30 x 12 = 360 months)
I/YR: 8.5 (The investment yields 8.5% per year)
PV: -94,069.21 (This is the result from Step 1)
PMT: 0 (Angela doesn't invest anything more for the remaining 30 years)
FV: (This is what I'm trying to find)
**Step 1: How much does Bill have at the end?**
N: 360 (After doing not investing for the first 10 years, Bill invests every month for 30 years, which is 30 x 12 = 360 months)
I/YR: 8.5 (The investment yields 8.5% per year)
PV: 0 (Bill starts with nothing)
PMT: -500 (Bill invests $500 per month)
FV: (This is what I'm trying to find)
**Step 4: Who did better?**
At retirement, Angela has $1,193,973.31 and Bill has $825,352.86.
*three times as much* as Angela, and ended up with $368K less!

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- Find out how much Angela has after 10 years.
- Find out how much Angela has at the end.
- Find out how much Bill has at the end.
- Find out who has more, and how much more they have.

After 10 years of investing, Angela has **$94,069.21**.

At retirement, Angela has **$1,193,973.31**.

At retirement, Bill has **$825,352.86**.

So Angela retires with $1,193,973.31 - $825,352.86 = **$368,620.45** more than Bill.

Have you started saving for retirement? If not, why not? If so, did you start early, or are you trying to play catch-up? Let us know in the comments!