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.
#1
Hard to tell. Were there no payments made?
If none were made then ....
x(1.056)^4 = 8,996.32
solve for x
#2
current value = 1000000(.96)^5
= ....
(time to get out of that investment)
To find the initial value of the car loan, we need to use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
where:
A is the final amount ($8,996.32)
P is the principal (initial value of the loan, what we want to find)
r is the interest rate (5.6% or 0.056)
n is the number of times interest is compounded per year (since it's yearly, n = 1)
t is the number of years (4)
We can rearrange the formula to solve for P:
P = A / (1 + r/n)^(n*t)
Using the given values:
P = $8,996.32 / (1 + 0.056/1)^(1*4)
P = $8,996.32 / (1.056)^4
P ≈ $7,597.26
Therefore, the initial value of the car loan was approximately $7,597.26.
Now, let's move on to the second question about the investment in the stock market.
To find the current value of the $1,000,000 investment after decreasing 4% annually for 5 years, we can use the formula for compound interest in reverse:
A = P * (1 + r/n)^(n*t)
In this case, we want to find the final amount (A) when the principal (P) is $1,000,000, the interest rate (r) is -4% (since it's decreasing), the number of times compounded per year (n) is 1 (since it's yearly), and the duration (t) is 5 years.
A = $1,000,000 * (1 - 0.04/1)^(1*5)
A = $1,000,000 * (0.96)^5
A ≈ $814,027.61
Therefore, the current value of the $1,000,000 investment after decreasing 4% annually for 5 years is approximately $814,027.61.