Math Snap

STEP 1

Assumptions1. The original amount in the investment account is $7800. The increase in the account over one year is7%
3. The increase is calculated as a one-time payment, not monthly compounding4. The year-end amount is the original amount plus the increase

STEP 2

First, we need to express the percentage increase as a decimal. We can do this by dividing the percentage by100.
$$Percentage\, increase\, as\, decimal = \frac{Percentage\, increase}{100}$$

STEP 3

Now, plug in the given value for the percentage increase to calculate the decimal equivalent.
$$Percentage\, increase\, as\, decimal = \frac{7\%}{100}$$

STEP 4

Calculate the decimal equivalent of the percentage increase.
$$Percentage\, increase\, as\, decimal = \frac{7}{100} =0.07$$

STEP 5

Now, we can fill in the blank in the equation for the year-end amount. The year-end amount is the original amount plus the percentage increase, expressed as a decimal.
$$Year-end\, amount = (1 + Percentage\, increase\, as\, decimal) \times Original\, amount$$

STEP 6

Plug in the decimal equivalent of the percentage increase into the equation for the year-end amount.
$$Year-end\, amount = (1 +0.07) \times Original\, amount$$

STEP 7

implify the equation for the year-end amount.
$$Year-end\, amount =1.07 \times Original\, amount$$

STEP 8

Now, we can use the equation for the year-end amount to calculate the actual amount in Raina's account at the end of the year. Plug in the original amount into the equation.
Year-end\, amount =1.07 \times \($\)7800

Calculate the year-end amount.
Year-end\, amount =.07 \times \($\)780 = \($\)8346The year-end amount in Raina's account is $8346.