An amount of k20.000 is invested for 5 years in a credit union which pays an annual untreated rate of 4.5 percent. Find accumulated value after 4 years if intrest rate is
a: annually
b:semi annually
c:quarterly
e:monthly
To find the accumulated value after 4 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated value
P = 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
Let's calculate the accumulated value for each scenario:
a) Annually (once a year):
A = 20,000(1 + 0.045/1)^(1*4)
A ≈ 20,000(1.045)^4
A ≈ 23,221.87
b) Semi-annually (twice a year):
A = 20,000(1 + 0.045/2)^(2*4)
A ≈ 20,000(1.0225)^8
A ≈ 23,252.33
c) Quarterly (four times a year):
A = 20,000(1 + 0.045/4)^(4*4)
A ≈ 20,000(1.01125)^16
A ≈ 23,265.09
e) Monthly (twelve times a year):
A = 20,000(1 + 0.045/12)^(12*4)
A ≈ 20,000(1.00375)^48
A ≈ 23,271.95
Therefore, the accumulated value after 4 years will be approximately:
a) Annually: $23,221.87
b) Semi-annually: $23,252.33
c) Quarterly: $23,265.09
e) Monthly: $23,271.95