Streams of payments, priced in one number.
Perpetuities, annuities and loans are just many payments brought back to today. Learn the shortcuts, then the rate traps: APR or EAR, which period, and real or nominal.
A stream of payments: bring each one back on its own
A stream of payments: bring each one back on its own
| Year | Paid | Divide by | Worth today |
|---|---|---|---|
| 1 | $4,000.00 | 1.081 | $3,703.70 |
| 2 | $6,000.00 | 1.082 | $5,144.03 |
| 3 | $2,500.00 | 1.083 | $1,984.58 |
| 4 | $10,000.00 | 1.084 | $7,350.30 |
| Total | $22,500.00 | $18,182.62 |
Two offers, a retirement goal and a scholarship
- Which offer is better? Justify it with effective annual rates.
- For the rest of the question Priya takes the better offer. How much will she have at 65? Split the interest she earns into simple interest and interest on interest.
- Priya wants $1,800,000.00 at 65. Is the lump sum enough? If not, what equal amount must she add at the end of every quarter, starting three months from now, in the same account?
- At 75 she will move money into a foundation account earning 6.5% a year, compounded annually. It pays a scholarship one year later of $36,000.00, growing 2% a year forever. How much must go into the foundation at 75?
- Until 75 that money stays in her retirement account. What share of her $1,800,000.00 at 65 must she set aside for the foundation?
Midterm coming up and annuities still feel slippery?
Bring your problem sets. We work through them together until every type feels routine.
Questions, answered.
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