8.find the amount to be invested now at 6% compounded monthly so as to accumulate $8888 in three years.
solution :
p=8888
i=6%
t= 3/360=0.0008
$8888(e^0.06(0.25))
=9022.32
the answer is $ 7427.21
NO
you used the concept of continuous compounding
but it said it was compounded monthly
Even with the above in consideration your expression of
8888(e^0.06(0.25))
makes absolutely no sense.
i = .06/12 = .005
n = 3(12) = 36 months
PV = 8888(1.005)^-36
= $7427.21
For a single investment, there is one main formula:
Amount = PV (1+i)^n <------> PV = Amount (1+i)^-n
where i is the periodic rare, and n is the number of interest periods
for annuity you have
Amount = payment ( (1+i)^n - 1)/i
Present value = payment ( 1 - (1+i)^-n)/i
The vast majority of compound interest problems are handled with these 3 formulas.
Memorize them.
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To calculate the amount to be invested now at 6% compounded monthly to accumulate $8888 in three years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future amount ($8888 in this case)
P = the principal amount to be invested
r = annual interest rate (6% or 0.06 as a decimal)
n = number of times compounding occurs per year (monthly compounding, so n = 12)
t = number of years (3 years in this case)
We need to solve for P in this equation. Plugging in the given values, we have the equation:
8888 = P(1 + 0.06/12)^(12*3)
To solve for P, we can divide both sides of the equation by (1 + 0.06/12)^(12*3):
8888 / (1 + 0.06/12)^(12*3) = P
Calculating the right side of the equation, we get:
P = approximately $7427.21
Therefore, the amount to be invested now at 6% compounded monthly to accumulate $8888 in three years is $7427.21.