Trevor has an investment worth $6,774.50. He made his only deposit in it 22 years ago. Given that the investment yields 2.7% simple interest annually, how big was the initial deposit?
The correct answer and explanation is:
To find the initial deposit (principal) Trevor made 22 years ago, given the current value and interest rate under simple interest, we use the simple interest formula: A=P(1+rt)A = P(1 + rt)
Where:
- AA is the final amount (total value of the investment) = $6,774.50
- PP is the principal (initial deposit) = ?
- rr is the annual interest rate = 2.7% = 0.027
- tt is the time in years = 22
Step 1: Plug into the formula
6,774.50=P(1+0.027×22)6,774.50 = P(1 + 0.027 \times 22)
Step 2: Calculate the interest term
0.027×22=0.5940.027 \times 22 = 0.594 1+0.594=1.5941 + 0.594 = 1.594
Step 3: Solve for PP
6,774.50=P×1.5946,774.50 = P \times 1.594 P=6,774.501.594P = \frac{6,774.50}{1.594} P≈4,248.68P \approx 4,248.68
✅ Final Answer:
Trevor’s initial deposit was approximately $4,248.68.
📘 Explanation (300 words):
Simple interest is a method of calculating interest where the interest amount is based only on the original principal over a period of time. The formula A=P(1+rt)A = P(1 + rt) combines the principal, the interest rate per year, and the time in years to determine the total accumulated amount.
In Trevor’s case, the current investment is worth $6,774.50 after 22 years, and the interest rate is 2.7% per year. Since he made only one deposit, the only way this amount could grow is through accumulating interest on the original amount each year, without compounding.
Using the formula, we calculated the total growth multiplier as 1+(0.027×22)=1.5941 + (0.027 \times 22) = 1.594. This means his investment grew by about 59.4% over the 22 years. To find the original investment, we reversed the process by dividing the final amount by the multiplier: 6,774.50÷1.594≈4,248.686,774.50 \div 1.594 \approx 4,248.68.
This tells us that Trevor initially deposited about $4,248.68, and over 22 years, it earned about $2,525.82 in interest (6,774.50 – 4,248.68), thanks to the consistent simple interest rate of 2.7%.
This calculation is crucial in financial planning and shows how interest rates and time affect investment growth, especially under different interest models like simple or compound interest.