Michael invests 200 dollars in an account that pays an annual interest rate of five percent, compounded monthly. Write an equation he could use to work out 𝑉, the value of his investment in three years’ time.
In order to answer this question, we need to use the general formula for compound interest for a value of an investment compounded 𝑛 times per year. This value 𝑉 is equal to 𝑃 multiplied by one plus 𝑟 over 100 divided by 𝑛 all raised to the power of 𝑦 multiplied by 𝑛. 𝑃 is the principal value or initial investment. 𝑟 is the interest rate as a percentage. 𝑛 is the number of compound periods per year. And finally, 𝑦 is the number of years.
In this question, we want to write an equation for 𝑉, where 200 dollars is the initial investment. The interest rate is five percent, and this interest is compounded monthly. We are asked to calculate the value of the investment in three years’ time. This gives us an equation 𝑉 is equal to 200 multiplied by one plus five over 100 divided by 12 all raised to the power of three multiplied by 12. Five over 100 or five one hundredths divided by 12 can be rewritten as five over 1200. Multiplying the exponents three and 12 gives us 36.
𝑉 is, therefore, equal to 200 multiplied by one plus five over 1200 all raised to the power of 36. This is an equation that Michael could use to work out the value of 𝑉. Whilst we are not asked to in this question, we could type this into the calculator, giving us a value of 𝑉 of 232.2944 and so on. To two decimal places, this is equal to 232.29.
The value of Michael’s investment after three years would be 232 dollars and 29 cents.