Question

# The simple interest earned by an account varies jointly as the time and the principal. In 2 years, a principal of $5000 earns $650 interest. How much would $1000 earn in 1 year?

Answer

$0.01

- Q:What is the formula for simple interest? A:The formula for simple interest is I = prt, where I is the amount of interest, p is the principal or amount of the loan, r is the annual interest rate, and t is the amount of time in years.
- Q:What is the joint variation formula? A: The joint variation formula is y=kxz, where y is the dependent variable, x and z are the independent variables, and k is a constant of variation.
- Q:How can we use the given information to find the interest rate? A:Using the simple interest formula, we can solve for the interest rate as r=I/pt. In this case, I=$650, p=$5000, and t=2 years, so r=$650/(2*$5000)=.065, or 6.5%.
- Q:Using the joint variation formula, how much would $1000 earn in 1 year? A:Using k=r/p, we have k=.065/$5000=.000013. Then using y=kxz, we can solve for y as $1000=y*(1*.000013), which simplifies to y=$0.013, or $0.01 rounded to the nearest cent.