We would apply the formula for finding compound interest which is expressed as
A = P(1 + r/n)^nt
Where
A is the final amount after t years
P is the initial amount or capital
t is the number of years
n is the number of compounding
r is the interest rate
From the information given,
p = 10000
t = 7
r = 4.5/100 = 0.045
a) for semiannual compounding, n = 2(twice a year)
Thus,
A = 10000(1 + 0.045/2)^2 * 7
A = 13654.83
b) for quarter compounding, n = 4(there are 4 quarters in a year)
Thus,
A = 10000(1 + 0.045/4)^4 * 7
A = 13678.52
c) for monthly compounding, n = 12(there are 12 months in a year)
Thus,
A = 10000(1 + 0.045/12)^12 * 7
A = 13694.52
d) For continuous compounding, the formula is
A = pe^rt
A = 10000 * e^(0.045 * 7)
A = 13702.59