8. A balance of $5,500.00 principal earns 3% interest, compounded annually. After 5 years, what is
the balance in the account?
9. A car costs $25,000 and depreciates in value by 15% each year. How much will the tractor be
worth after 4 years?
5500(1 + .03)^5
and
25000(1 - .15)^4
see how that works?
To calculate the balance in the account after 5 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the balance after time t
P = the principal amount
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per time period
t = the number of time periods
In this case:
P = $5,500.00
r = 3% or 0.03 (as a decimal)
n = 1 (compounded annually)
t = 5 years
Plugging in these values into the formula:
A = $5,500.00(1 + 0.03/1)^(1*5)
= $5,500.00(1 + 0.03)^5
= $5,500.00(1.03)^5
= $5,500.00(1.159274074)
≈ $6,375.01
Therefore, the balance in the account after 5 years would be approximately $6,375.01.
To calculate the worth of the car after 4 years, we can use the formula for depreciation:
W = P(1 - r)^t
Where:
W = the worth after time t
P = the initial value
r = the depreciation rate (as a decimal)
t = the number of time periods
In this case:
P = $25,000
r = 15% or 0.15 (as a decimal)
t = 4 years
Plugging in these values into the formula:
W = $25,000(1 - 0.15)^4
= $25,000(0.85)^4
= $25,000(0.52200625)
≈ $13,050.16
Therefore, the car will be worth approximately $13,050.16 after 4 years.
To find the balance in the account after 5 years with a 3% interest rate, compounded annually, you can use the formula for compound interest:
Balance = Principal * (1 + Interest Rate)^Number of Years
In this case, the principal is $5,500.00, the interest rate is 3%, and the number of years is 5.
Substituting the values into the formula:
Balance = $5,500.00 * (1 + 0.03)^5
To solve this calculation step by step:
1. Add 1 to the interest rate: 1 + 0.03 = 1.03
2. Raise 1.03 to the power of 5: 1.03^5 = 1.159274074.
Finally, multiply the result by the principal:
Balance = $5,500.00 * 1.159274074
The balance in the account after 5 years is approximately $6,375.01.
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To find the worth of the car after 4 years with a 15% annual depreciation rate, you can use the formula for compound depreciation:
Worth = Initial Value * (1 - Depreciation Rate)^Number of Years
In this case, the initial value of the car is $25,000, the depreciation rate is 15%, and the number of years is 4.
Substituting the values into the formula:
Worth = $25,000 * (1 - 0.15)^4
To solve this calculation step by step:
1. Subtract the depreciation rate from 1: 1 - 0.15 = 0.85
2. Raise 0.85 to the power of 4: 0.85^4 = 0.52200625.
Finally, multiply the result by the initial value:
Worth = $25,000 * 0.52200625
The worth of the car after 4 years is approximately $13,050.16.