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QuestionRaina invested \$7800 and it increased by 7%.
(a) Year-end amount as a decimal: Year-end amount = 1.07 × Original amount. (b) Calculate the year-end amount in Raina's account: Year-end amount: \$

Studdy Solution

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=Percentage increase100Percentage\, 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=7%100Percentage\, increase\, as\, decimal = \frac{7\%}{100}

STEP 4

Calculate the decimal equivalent of the percentage increase.
Percentage increase as decimal=7100=0.07Percentage\, 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)×Original amountYear-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)×Original amountYear-end\, amount = (1 +0.07) \times Original\, amount

STEP 7

implify the equation for the year-end amount.
Year−end amount=1.07×Original amountYear-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×$7800Year-end\, amount =1.07 \times \$7800

STEP 9

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

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