Question Video: Creating Exponential Equations and Using Them to Solve Problems

When Matthew was born, his grandparents invested $500 in a fund that would mature on his 21st birthday. If the fund earned 6% per year, compounded annually, how much was its value when it matured? Give your answer to the nearest dollar.

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Video Transcript

When Matthew was born, his grandparents invested 500 dollars in a fund that would mature on his 21st birthday. If the fund earned six percent per year compounded annually, how much was its value when it matured? Give your answer to the nearest dollar.

In order to calculate the new value, we need to identify three things: the original value, the multiplier, and the number of payments. We will then multiply the original value by the multiplier to the power of the number of payments.

The original value in this case is 500 dollars, the amount of his grandparents invested. The multiplier is 1.06 as the interest was six percent per annum. Adding six percent to a 100 percent, as it’s an increase, will give us a 106 percent. This is the same as 1.06 as a decimal.

As the interest is compounded annually and the fund will mature on his 21st birthday, the number of payments will be 21. Substituting these values into the formula or equation gives us 500 multiplied by 1.06 to the power of 21.

Typing this into the calculator gives us a new value, after 21 years, of 1699.7818. As we have more than 50 cents, we’ve round this up to the nearest dollar, giving us a value of 1700 dollars.

Therefore, the value of the fund when it matures is seventeen hundred dollars or one thousand seven hundred dollars.

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