CHAPTER 5

Mathematics of Individual Finance

[Mathematics of Individual Finance Page 1] [Time Value Of Money][Future Values] [More Frequent Compounding] [Effective Annual Interest Rate] [Present Value]
[Annuities] [Present Value Of An Annuity] [Annuities Due] [Future Value Of An Annuity] [Determining Payments] [Bond Valuation]
[Uneven Cash Flows] [Amortization Schedule] [Household Capital Budgeting] [Duration] [Summary] [Discussion Questions]
[Problems]

More Frequent Compounding

In the days before computers, it was common for banks to compound only annually, and customers who withdrew funds before the anniversary of their deposit would often forego interest for that entire year. With computers available everywhere, interest is often compounded and credited to the account on a daily basis. However, quarterly, monthly and even weekly compounding may still be found.

To calculate the future value of a present sum which is compounded more than once a year, you need to multiply the number of annual periods by the number of times the interest is compounded in a year.

n = number of years x number of compounding periods in a year

You must also divide the annual rate of interest by that same number of compounding periods in a year.

r = annual rate of interest / number of compounding periods in a year

Example 5-2

Ed deposits $11,280 in a bank account paying 4% per year, compounded and credited quarterly. How much will he have at the end of 3 years?

Solution 5-2

The number of total periods (quarters, in this case) is 3 years times 4 or 12 which is n. The interest rate paid per quarter is 4% divided by 4 or 1%. Therefore,

FV12= $11,280(1.01)12
= $11,280(1.1268)
= $12,710.30

You will note on Table A-3 that 1.1268 is the future value interest factor. However, you will also note that the use of the table is limited by the fact that only whole rates of interest are given. If we were to compound other than quarterly, semi-annually or annually, we would not be able to use the table without difficult and inexact interprelation.

On a finance calculator [12 N 1 %i 11280 PV CPT FV] the answer is $12,710.59, demonstrating the sizeable rounding errors generated by use of the tables.

Example 5-3

Tim puts $52,340 into a brokerage money market account that pays an annual rate of interest of 3.4% compounded and credited daily. How much would Tim have at the end of 90 days?

Solution 5-3

Using a 365 day year, the number of periods per year is 365 and the interest rate per period is 3.4%/365 = .009315%. On a financial calculator [90 N .009315 %i 52340 PV CPT FV] the answer is $52,780.62. Note that on the finance calculator, the division of 3.4% by 365 could have been done right before pressing %i. The keystrokes would have been [90 N 3.4/356 = %i 52340 PV CPT FV].

[Effective Annual Interest Rate]

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