In 5.03 we varied the frequency of the compounding periods and saw that the greater the frequency, the greater the interest earned. Here we will explore how the term of the loan and the interest rate rate affect the interest paid on an investment.
Increasing the interest rate associated with an investment, or increasing the amount of time we leave our money in the investment, will lead to an increase in its future value. But which change will have a bigger impact?
The answer will depend on the particular values and context of our situation, so let's look at some examples.
Worked examples
Question 1
Elizabeth has $\$2000$$2000 in a savings account which earns $1%$1% interest per annum, compounded annually.
What is the future value of her savings account in $5$5 years? Round your answer to the nearest cent.
Calculate the future value if the interest rate is doubled over the same period.
Calculate the future value if the term of the investment is doubled for the original interest rate.
Compare the interest earned in both situations. Which has a greater impact?
Doubling the term
ADoubling the interest rate
B
Question 2
Victoria is considering whether she should invest her money now rather than $8$8 years down the track. For an initial investment of $\$4000$$4000, the formula $FV=4000\left(1.029\right)^n$FV=4000(1.029)n models the value her money will grow to in $n$n years.
What is the interest rate paid on the investment? Give your answer as a percentage.
How many times larger will her balance be if she starts investing now rather than $8$8 years down the track? Give your answer correct to two decimal places.
Calculate the difference in the interest accrued, to the nearest dollar, if Victoria invested now rather than in $8$8 years.
Find the least number of whole years for the investment to double.