Compute the amount of compound interest earned in 1 year for an investment of $1,000,000 with a nominal interest rate of 8% compounded quarterly.
P = Po(1+r)^n.
Po = $1,000,000.
r = (8%/4)/100% = 0.02 = Quarterly % .rate expressed as a decimal.
n 4Comp./yr. * 8trs = 32 Compounding
periods.
Plug the above values into the given Eq and solve for P.
I = P-Po.
CORRECTION: n = 4Comp./yr. * 1yr. = 4
Compounding periods.
To calculate the compound interest earned on an investment, we need to use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount after interest
P = the principal amount (initial investment)
r = the nominal interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $1,000,000, the nominal interest rate (r) is 8% or 0.08, the interest is compounded quarterly, so n = 4, and the time period (t) is 1 year.
Plugging in the values into the formula, we have:
A = $1,000,000 * (1 + 0.08/4)^(4*1)
Simplifying the equation:
A = $1,000,000 * (1 + 0.02)^4
Calculating the exponential part:
A = $1,000,000 * (1.02)^4
A = $1,000,000 * 1.082432
A = $1,082,432
To find the compound interest earned in one year, we subtract the principal amount from the final amount:
Interest earned = A - P
Interest earned = $1,082,432 - $1,000,000
Interest earned = $82,432
Therefore, the compound interest earned in one year for an investment of $1,000,000 with a nominal interest rate of 8% compounded quarterly is $82,432.