Antique Car

2. An antique car boutght for $8400 in 1950 sould for $590,000 in 1982. What was the annual interest rate?

how long would it take $1000 invested at 4% compounded annually to double itself

3. for every metre below the water surface, the light intensity is reduced by 2.5% at what depth is it 10% of surface intensity?

how long would it take $1000 invested at 4% compounded annually to double itself.

Solution:
$1,000 invested at 4 percent compounded annually, and you want to know how long it will take for your money to double. You can use the formula for future value to solve this

problem.

FV = C0 × (1 + r)^N

FV = future value
C0 = initial investment
r = periodic rate of interest, which is calculated as
N = number of periods

Using the information in the example above, determine the values for each variable or constant.

FV = $2,000 (the initial investment doubled)
C0 = $1,000
r = 0.04/1 (4% compounded once a year)
N = number of periods

To find the value of N, you will need to use logarithms. First, simplify the equation and divide each side by 1,000. Then take the logarithm of each side of the equation. Once

you have done that, you can further simplify the equation by applying the law of logarithms that states that the logarithm of a power is the exponent times the logarithm of the

base.

FV = C0 × (1 + r)^N
2000 = 1000 x (1 + 0.04/1)^N
2000 = 1000 x (1.04)^N
2000/1000 = (1000 x (1.04)^N)/1000
2 = (1.04)^N
log 2 = log (1.04)^N
log 2 = N log (1.04)
N = log 2/ log (1.04)
N = 0.3010/0.0170
N = 17.70
It will take 17.70 years for your investment to double if invested at an annual rate of 4 percent compounded annually.

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