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?
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.
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explain the steps of how to solve these two question's
Surely you have a calculator.
To find the initial value of the loan, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final balance of the loan ($8,996.32 in this case)
P = Principal or initial value of the loan (what we are trying to find)
r = Annual interest rate (5.6% = 0.056)
n = Number of times the interest is compounded per year (since it's compounding annually, n = 1)
t = Time in years (4 years in this case)
Now we can rearrange the formula to solve for P:
P = A / (1 + r/n)^(nt)
Substituting the given values:
P = 8,996.32 / (1 + 0.056/1)^(1*4)
Simplifying the denominator:
P = 8,996.32 / (1 + 0.056)^4
Calculating the exponent:
P = 8,996.32 / (1.056)^4
Solving for P:
P ≈ 7,605.27
Therefore, the initial value of the car loan was approximately $7,605.27.