(Interest Rate Word Problems)
1. To solve an exponential or logarithmic word problems, convert the narrative to an equation and solve the equation.
Problem 2: If you invested $1,000 in an account paying an annual
percentage rate (quoted rate) of 12%, compounded weekly, how
much would you have in you account at the end of 1 year, 10 years,
20 years, 100 years?
Answer: 1 year = $1,127.34,10 Years = $3,315.53, 20 years
= $10,992.74, 100 years = $160,520,208.47
Solution and Explanations:
where A is the balance at the end of a certain time period, P is the beginning investment of $1,000, t is the number of years. The annual rate of 12% is converted to a weekly interest rate since the compounding is weekly (52 times per year). Take the annual interest rate of 12% and divide by 52 to obtain the weekly interest rate. The exponent is 52t because there are 52 compounding periods in every year. Therefore, 52t represents the number of compounding periods during t years.
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Author: Nancy Marcus