If $100 is invested at 6% compunded
A - annually
B - quarterly
C - monthly
what is the amount after 4 years? How much interest is earned?
0.5
A. Pt = Po*(1+r)^n.
r = 6%/100% = 0.06 = Annual % rate expressed as a decimal.
n = 1 comp./yr * 4 yrs = 4 compounding
periods.
Pt = 100*(1.06)^4=$126.25 After 4 yrs.
Int. = Pt - Po = 126.25 - 100 = $26.25.
B. Pt = Po*(1+r)^n.
r = (6%/4) / 100% = 0.015 = Quarterly
% rate expressed as a decimal.
n = 4 comp./yr. * 4yrs = 16 compounding
periods. Calculate Pt and Int.
C. Pt = Po*(1+r)^n.
r = (6%/12) / 100% = 0.005 = Monthly %
rate expressed as adecimal.
n = 12 comp./yr * 4yrs = 48compounding
periods. Calculate Pt and Int.
To calculate the amount after 4 years and the interest earned, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
Given:
P = $100
r = 6% (or 0.06 in decimal form)
t = 4 years
Let's calculate the amount for each compounding period:
A) Annually (n = 1):
A = 100(1 + 0.06/1)^(1*4)
B) Quarterly (n = 4):
A = 100(1 + 0.06/4)^(4*4)
C) Monthly (n = 12):
A = 100(1 + 0.06/12)^(12*4)
To find the interest earned, subtract the initial investment from the final amount:
Interest earned = A - P
Now, let's calculate the amount and interest earned for each case (annually, quarterly, monthly).