Josiah invests $360 into an account that accrues 3% interest annually. Assuming no deposits or withdrawals are made, which equation represents the amount of money in Josiah's account, $y$, after $x$ years?
A. $y=360(1.3)^x$
B. $y=360(0.3)^x$
C. $y=360(0.03)^x$
D. $y=360(1.03)^x
Answer (2)
The problem involves finding the equation for compound interest.
The compound interest formula is A = P ( 1 + r ) x .
Substitute the given values: P = 360 and r = 0.03 .
The equation representing the amount of money after x years is y = 360 ( 1.03 ) x .
Explanation
Understanding the Problem We are given an initial investment of 360 t ha t a ccr u es 3 y , a f t er x$ years, assuming no deposits or withdrawals are made.
Recalling the Compound Interest Formula The formula for compound interest is: A = P ( 1 + r ) x where:
A is the amount of money accumulated after x years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (as a decimal).
x is the number of years the money is invested or borrowed for.
Identifying the Values In this problem:
P = 360 (the initial investment)
r = 0.03 (3% annual interest rate expressed as a decimal)
x is the number of years
y is the amount of money after x years, so A = y .
Applying the Formula Substitute the given values into the compound interest formula: y = 360 ( 1 + 0.03 ) x Simplify the expression inside the parentheses: y = 360 ( 1.03 ) x
Final Answer Therefore, the equation that represents the amount of money in Josiah's account after x years is: y = 360 ( 1.03 ) x This matches the fourth option provided.
Examples
Imagine you deposit $360 into a savings account that offers a 3% annual interest rate. This equation helps you predict how much money you'll have in the account after a certain number of years, assuming you don't make any additional deposits or withdrawals. For example, after 5 years, you would have approximately $360 * (1.03)^5 = $416.46. This type of calculation is essential for financial planning and understanding the growth of investments over time.
The equation representing the amount of money in Josiah's account after x years of investment at 3% interest is y = 360 ( 1.03 ) x . This is derived from the compound interest formula. Thus, the correct option is D.
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