3-3-1 - 3-3 Part I Annuities Ordinary annuity • a...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 3-3 Part I Annuities Ordinary annuity • a sequence of equal periodic payments • made at the end of each payment period Example: an annuity of 4 payments of $100 per month end of month 1 pay $100 end of month 2 pay $100 end of month 3 pay $100 end of month 4 pay $100 Question: How much is the annuity worth (its future value) at the end of 4 months? Assume payments are being placed into a savings account at 12%. We use the following symbols: PMT = the periodic payment i = interest rate per period n = number of payments FV = amount (future value of the annuity) The general formula is: (1 + i ) n − 1 FV = PMT = PMT s i n i “s angle n at i” 1.014 − 1 so our FV = 100 1.01 − 1 = $406.04 3-3 Part I p. 1 Example: you need $18,000 in three years to buy a car. How much per month should you put into a 6% savings account to accumulate that amount? (1.005) 36 − 1 18000 = PMT .005 can you solve it? ($457.59) Creating a schedule (by period) We can easily compute the future value of a series of payments using the future value formula. Suppose we want a more detailed report, period by period, that shows: • interest being earned each period • the value of the investment at the end of each period This kind of schedule can be created as follows. We will use our example of 4 monthly payments of $100, earning a nominal 12% (i = .01) interest earned end PMT during month month = i(prev FV) 1 100 0 2 100 1.00 3 100 2.01 4 100 3.03 3-3 Part I FV (end of month) = (prev FV) + PMT + interest 100.00 201.00 303.01 406.04 p. 2 Creating a schedule (by year) Compute FV at end of each year by using the formula (1 + i ) n − 1 FV = PMT i Compute interest earned during year (e.g., for income tax purposes) as follows: FV = (prev FV) + payments + interest interest = FV - (prev FV) - payments end FV (use formula) year 100((1.01)12-1)/.01 1 = 1268.25 100((1.01)24-1)/.01 2 = 2697.35 3 4307.69 3-3 Part I Payments Interest = FV – (prev FV) - Payments 1200 68.25 1200 229.10 1200 410.34 p. 3 ...
View Full Document

This note was uploaded on 12/11/2011 for the course MATH 1324 taught by Professor Staff during the Spring '11 term at Austin Community College.

Page1 / 3

3-3-1 - 3-3 Part I Annuities Ordinary annuity • a...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online