Question

Beverly and Kyle Nelson currently insure their cars with separate companies, paying $580 and $615 a year. If they insured both cars with the same company, they would save 20 percent on the annual premiums.

What would be the future value of the annual savings over 10 years based on an annual interest rate of 6 percent?

Answer 1

The question involves calculating the annual savings on car insurance premiums by insuring both cars under one company, saving 20%, and then determining the future value of these savings over 10 years at a 6% interest rate using the future value of an annuity formula.

Step-by-step explanation:

Firstly, let's calculate the total annual premium that Beverly and Kyle pay separately: $580 + $615 = $1195. If they save 20%, they will be saving 0.20 × $1195 = $239 per year. To find the future value of these annual savings over 10 years at a 6 per cent interest rate, we use the future value of an annuity formula:

FV = P × [((1 + r)^n - 1) / r]

Where P is the annual payment (savings here), r is the interest rate per period, and n is the number of periods. Plugging in the values we get: FV = $239 × [((1 + 0.06)^{10} - 1) / 0.06]. By calculating the expression within the brackets and then multiplying by $239, we find the future value of Beverly and Kyle's savings.

The result will display the future value of the savings they could invest for a 10-year period, which shows how this saving can grow over time thanks to the power of compounding interest.