Since 2007, a particular fund returned 13.8% compounded monthly. How much would a $4000 investment in this fund have been worth after 4 years?
P = Po*(1+r)^n
Po = $4000 = Initial principal.
r = (13.8%/12)/100% = 0.0115 = Monthly %
rate expressed as a decimal.
n = 12Comp/yr. * 4yrs. = 48 Compounding
periods.
Solve for Principal(P).
To find out how much a $4000 investment would be worth after 4 years with a compounded monthly return of 13.8%, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, the annual interest rate is 13.8%, which is equivalent to 0.138 as a decimal. Since the interest is compounded monthly, n = 12. And the investment is for 4 years, so t = 4.
Plugging in the values into the formula:
A = 4000(1 + 0.138/12)^(12*4)
Now, let's calculate the final amount:
A = 4000(1 + 0.0115)^(48)
A ≈ $6367.99
Therefore, a $4000 investment in this fund would have been worth approximately $6367.99 after 4 years.