Effective Interest Calculation

A student added this a few years ago. There is plenty wrong with it. Do not try to follow the example. I am keeping the frame to fix it at a later date.

Question

Your very superstitious grandmother has offered to place $444.44 into a bank account for your college education fund every quarter. The number four is the lucky number she read in her tea leaves on the day of your birth, and her organic all natural holistic palm reading life adviser explained the secret to happiness is linked to your college education and the number four. She will make the payments starting on your first birthday and will stop payments when you reach eighteen. What is the future worth at the end of of the payment cycle if the interest rate for the account is 4.44% and it was compounded:

a) Quarterly?

b) Monthly?

Answer

First let's pull out the important information

Payments of $444.44 will be made every 3 months (Quarterly)

Interest rate is 4.44% / year (this is the standard reporting from banks for interest rates)

r = 0.0444, N = 18 years * 4 quarters/year = 72

Next let's obtain the equations we will need to solve the problem

i = [(1 + (r/(C)(K)))^C] - 1
where
r = interest rate / year
C = number of interest periods / payment period
K = number of payments / year

F = A[ ((1 + i)^N - 1) / (i)]

Now find the interest rate for each condition and the corresponding future worth

a) Quarterly = 4 payments / year

i = [(1 + (0.0444/(1)(4)))^(1)] - 1
i = 0.0111

F = 444.44(F\A, i = 0.0111, N = 72)
F = $48607.78

b) Monthly = 12 payments / year

i = [(1 + (0.0444/(3)(4)))^(3)] - 1
i = 0.01114

F = 444.44(F\A, i = 0.01114, N = 72)
F = $48687.37

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