q1.The balance on a car loan after 4 years is $8,996.32. The interest rate is 5.6% compounding annually. What was the initial value of the loan?
q2. An investment made in the stock market decreased at a rate of 4% per year for 5 years. What is the current value of the $1,000,000 investment? Include your calculations in your final answer.
q3. A new car is sold for its sticker value of $19,400. Three years later, the customer returns to the car dealership to trade the car in. She is told that her car now has a value of $12,105. What is the rate of decline in the value of the car? In your final answer, include all of your calculations.
To answer these questions, we need to use the formulas for compound interest, compound depreciation, and percentage change.
q1. To find the initial value of the car loan, we can use the formula for compound interest, which is:
A = P(1 + r/n)^(nt)
Where:
A = the final balance after the given time period (8,996.32 in this case)
P = the initial principal amount (the initial value we want to find)
r = the annual interest rate (5.6% in this case)
n = the number of times that interest is compounded per year (since it compounds annually, n = 1)
t = the number of years (4 in this case)
Plugging in the given values, the formula becomes:
8,996.32 = P(1 + 0.056/1)^(1 * 4)
Simplifying the equation and solving for P:
P = 8,996.32 / (1 + 0.056)^4
Using a calculator, we can find that the initial value of the loan (P) is approximately $7,667.14.
q2. To find the current value of the investment, we can use the formula for compound depreciation, which is:
A = P(1 - r/n)^(nt)
Where:
A = the final value after the given time period (the current value we want to find)
P = the initial investment amount ($1,000,000 in this case)
r = the annual depreciation rate (4% in this case, which means it decreases at a rate of 4% per year)
n = the number of times that depreciation is compounded per year (since it depreciates annually, n = 1)
t = the number of years (5 in this case)
Plugging in the given values, the formula becomes:
A = 1,000,000(1 - 0.04/1)^(1 * 5)
Simplifying the equation and solving for A:
A = 1,000,000 * (1 - 0.04)^5
Using a calculator, we can find that the current value of the investment (A) is approximately $820,480.
q3. To find the rate of decline in the value of the car, we can use the formula for percentage change, which is:
Rate of change = (new value - initial value) / initial value * 100
Plugging in the given values, the formula becomes:
Rate of change = (12,105 - 19,400) / 19,400 * 100
Simplifying the equation and solving for the rate of change:
Rate of change = -0.372 * 100
Using a calculator, we can find that the rate of decline in the value of the car is approximately -37.2%. Note that the negative sign indicates a decrease in value.
all of these % problems are pretty similar.
We've done several for you in the past, and yet you offer no indication that you are even trying to solve them. Where do you get stuck?