MAELEC 5Theory of Interest

2

of problems in interest

Examples

Compound Interest

Examples

Present Value and Compound Interest

Approximate Accumulation Method

Compound Interest

Examples

•Find the compound interest on Php1 000 at the end of 8 at 8 compounded quarterly.

•Find the compound amount and interest if Php15 000 is invested at an interest rate of 9% compounded annually for 3 years.

Approximate Accumulation Method

• It is used if the n is a fraction or not exact number of periods

Steps:1. Find the compound amount at the end of

the largest period 2. Accumulate the result obtained in step 1 for

the remaining time at simple interest at the given nominal rate.

Examples

•Accumulate Php18 000 for 7 years and 4 months at 8.2% compounded quarterly

•Find the compound amount if Php5 000 is invested for 3 years and 9 months at 12% compounded semi annually.

Present value

to get the present value or how much you need to put in the bank now to have a specified amount in the future.

Present Value

Compound discountthe difference between the nominal amount of a particular sum in the future and its present discounted value.

𝐶𝑜𝑚𝑝𝑜𝑢𝑛𝑑 𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡=𝐹𝑢𝑡𝑢𝑟𝑒𝑉𝑎𝑙𝑢𝑒−𝑃𝑟𝑒𝑠𝑒𝑛𝑡𝑉𝑎𝑙𝑢𝑒

Examples• Find the present value and compound discount of Php5 000 due in 4 years if money is worth 8% compounded semi annually.

• Suppose you are depositing an amount today in an account that earns 5% interest, compounded annually. If your goal is to have Php50 000 in the account at the end of six years, how much must you deposit in the account today? What is the compound discount?

•Find the present value of Php10 000 due in 3 years and 4 months at 11% compounded quarterly.