Question

Find the annual rate of growth (interest rate) on an account that was worth $200 in 1975 and $415.79 in 1990

Answer 1

Use the following model for compound interest:

A = P (1+r)^5, where A is the accumulated amount, P is the principal or original amount, r is the annual interest rate (as a decimal fraction), and t is the number of years that have elapsed.

Let 1975 be year 0, i. e., t=0; let 1990 be year 15 (15 years after 1975).

Here's what you have in year 0: $200=P(1+r)^0. Thus, P=$200.

Here's what you have in year 15: $415.79 = $200 (1+r)^15

Solve this equation for r (as a decimal fraction).

Answer 2

The percent change from one period to another is calculated from the formula:

Where:PR = Percent Rate
VPresent = Present or Future Value
VPast = Past or Present ValueThe annual percentage growth rate is simply the percent growth divided by N, the number of years.
(415.79-200)/200*100=107.89
The annual percentage growth rate is simply the percent growth divided by N, the number of years.

107.89/15=7.193