Thus far we have assumed a constant rate of interest for the entire duration of an investment. However, interest rates may change from time to time. Thus, a bank, which pays interest at 8% when a deposit is made, may, after a number of years, raise the rate to 9% and later on perhaps reduce it to 7%. The final compound amount is the product of the original principal and two or more factors of the form (1 + i)n or en, each with its proper value for I and n or r and t. This is best illustrated with the help of following examples.

Example. A man made a deposit of Rs. 2500 in a savings account. The deposit was left to accumulate at 6% compounded quarterly for the first 5 years and at 8% compounded
semiannually for the next 8 years. Find the compound amount at the end of 13 years.

Solution. For the first years, i = 0.06/4 = 0.015, n = 5(4) = 20. For the next 8 years, I = 0.08/2 = 0.04, n = 8(2) = 16. Hence the amount at the end of 13 years is:

S = 2500 (1.015)²⁰ (1.04)¹⁶
=2500 (1.34685) (1.87298)
= Rs. 6306.55 (app.)

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