You will be making monthly deposits of increasing size into a bank account for 5

Question

You will be making monthly deposits of increasing size into a bank account for 5 years. The account will earn continuously compounding interest each month. Every 3 months (i.e. every quarter) the interest rate will increase The initial deposit will be $243. At the beginning of each month thereafter, another deposit will be made increasing by size $20. The continuously compounded interest rate will be 7.03% per annum for the first quarter, but will then increase by 0.4% at the beginning of each subsequent quarter. Note that the rate is the same constant value for each of the 3 months in a given quarter. Create a spreadsheet with headings as shown: Timestep Initial rate Rate increase Initial Deposit 0.083333 your value your value> Increase in deposit your value> Rate DepositPrev Total with interest Total 0 -B7+$B$3 -C3 =E3 0 Each row of the table will represent a different month, with the first row being time zero Programming note: You will be reusing this spreadsheet and using Goal Seek in the next question. So you should use best practices by having all parameters in individual cells at the top of your spreadsheet. Then inside the table, all the formulas should contain cell references only; no constant numerical values, as illustrated above Suggestion: For ease in entering the formula for an increasing rate, the first three time steps have the identical rate, and then the rate in any later month equals the rate 3 months ago plus the increase At the end of 5 years, after your 61st deposit, how much money do you have? Answer correct to 2 decimals

Explanation / Answer

The following MATLAB code gives the amount of money after number of deposits:

clc;clear all;close all;
d(1)=243;r(1)=7.03;m(1)=d(1);
for i=1:60
d(i+1)=d(i)+20;
end
for j=1:20
r(j+1)=r(j)+0.4;
end
for k=1:60
m(k+1)=d(k+1)+(m(k)).*(1+(r(1+(floor((k-1)./4))))./100).^(1/12);
end
display(m);

The results are pasted on an excel sheet, with number of deposits on one column and the amount of money we have in another:

Thus, after 61st deposit, i.e., at the end of 5 years we have 63,277.7879766 dollars accurately.
Thus, answer correct to 2 decimals is 63,277.79 Dollars.

1 243 2 507.3796663 3 793.2603848 4 1100.764231 5 1430.013973 6 1781.580201 7 2155.252421 8 2551.163054 9 2969.445314 10 3411.158515 11 3875.655356 12 4363.079418 13 4873.575187 14 5408.801542 15 5967.567063 16 6550.027404 17 7156.339244 18 7788.875178 19 8445.789505 20 9127.25097 21 9833.429488 22 10567.52933 23 11326.93702 24 12111.83555 25 12922.40922 26 13762.8163 27 14629.55823 28 15522.83352 29 16442.84219 30 17394.82368 31 18374.27274 32 19381.40482 33 20416.43709 34 21485.82297 35 22583.92392 36 23710.97397 37 24867.20902 38 26060.43543 39 27283.74933 40 28537.40507 41 29821.65918 42 31145.8167 43 32501.57028 44 33889.19661 45 35308.97482 46 36771.86212 47 38268.00267 48 39797.69775 49 41361.25134 50 42971.43467 51 44616.69094 52 46297.34849 53 48013.73869 54 49780.61792 55 51584.56765 56 53425.94604 57 55305.11469 58 57238.9965 59 59212.14128 60 61224.94011 61 63277.78798  

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