Question 1 We\'ve seen in class that the accumulation function of a general annu

Question

Question 1 We've seen in class that the accumulation function of a general annuity can be represented recursively as Ak = (1 + ix)Ak-1 +pmtk, with Ao-prto. Using Excel or any computer language, find the one-year Future Value (FV) of an investment of $200, $300, $700, $500 at the beginning of each quarter, with nominal yearly interest rate 24% compounded monthly for the first 4 months and 2.7% after. Print your Excel table or, if you use a computer language, print your code and show the value of Ak for each k.

Explanation / Answer

Here initial investment = 200

For this interest will be paid for 1 quarter at 2.4% compounded monthly.

After 3 months principal and interest would be added and for the new amount, for 3 months again interest will be calculated.

So we can use excel sheet for this (enclosed below):

Compound interest per month is calculated as follows:

From 5th month onwards 1+ik= 1.002333.

Formula used is previous right end total * ik +Ak-1 = Ak

Interest 2.4% p.a Hence per month 2.4/12 =0.20 Compounded quarterly So For 200 compound interest = (1.002)200 200.4

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