Serge invests $700 at 5.75% per year,
compounded quarterly. When the account
is closed, its value will be $950. How long
will Serge’s money be invested?
950=700(1+.0575/4)^n
solve for quarters n.
take log of each side
log(950)=log(700)+n*log(1.0244)
solve for n.
It doesnt get me the right answer.
OOPs, typo
1 + .0575/4=1.0144
To find out how long Serge's money will be invested, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final account value
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Time the money is invested in years
In this case, we have:
P = $700
A = $950
r = 5.75% = 0.0575 (decimal form)
n = 4 (compounded quarterly)
Now, let's substitute these values into the formula and solve for t:
950 = 700(1 + 0.0575/4)^(4t)
Divide both sides of the equation by 700:
950/700 = (1 + 0.0575/4)^(4t)
Simplify further:
1.3571 = 1.014375^(4t)
Take the natural logarithm of both sides:
ln(1.3571) = ln(1.014375^(4t))
Using the exponential property of logarithms, we can bring the exponent down:
ln(1.3571) = 4t * ln(1.014375)
Now divide both sides by 4 * ln(1.014375):
t = ln(1.3571) / (4 * ln(1.014375))
Using a calculator, we can evaluate this expression to find the value of t, which represents the number of years Serge's money will be invested.