Question

Compare simple and compound interest (compounded annually) on a principal of $25,000 at an annual rate of 4%. Find the number of years it takes for the the difference of the TOTAL using Simple interest and TOTAL using compound interest (compounded annually) to reach more than $1000.

Answer 1

Solution :-

As we know the Simple interest is charged always on the Principal Amount so the Simple interest rate per year is Same

Therefore Simple interest every year = $25,000 * 4% = $1,000

And in Case of Compounding interest the interest rate is charged on the outstanding balance that is Principal Amount and interest due there on.

Compound Interest in first Year = $25000 * 4% = $1000

Balance due after 1st year = $25000 + $1000 = $26000

Compound Interest in Second Year = ( $25000 + $1000 ) * 4% = $1040

Balance due after second year = $26000 + $1040 = $27040

And So on.....

C D Τ Ε F H36 B 1 Compound Interest Table 2 Year Opening Balance 3 1 25000 2 26000 3 27040 28121.60 29246.46 30416.32 31632.98 32898.29 11 9 34214.23 12 13 Simple Interest Table 14 Year Opening Balance 25000 26000 27000 28000 29000 30000 31000 32000 33000 Interest 1000 1040 1081.60 1124.86 1169.86 1216.65 1265.32 1315.93 1368.57 Closing Balance 26000 27040 28121.60 29246.46 30416.32 31632.98 32898.29 34214.23 35582.80 1 1. Interest 1000 1000 1000 1000 1000 1000 1000 1000 1000 Closing Balance 26000 27000 28000 29000 30000 31000 32000 33000 34000 Year Coumpound 26000.00 27040.00 28121.60 29246.46 30416.32 31632.98 32898.29 34214.23 35582.80 Simple 26000 27000 28000 29000 30000 31000 32000 33000 34000 Difference 0.00 40.00 121.60 246.46 416.32 632.98 898.29 1214.23 1582.80

- fx H36 А 1 Compound 2 Year E 31 Opening Balance -25000 =D3 =D4 -D5 OU Interest =B3*4% =B4*4% =B5*4% =B6*4% =B7*4% =B8*4% =B9*4% =B10*4% =B11*4% Closing Balance =B3+C3 =B4+C4 =B5+C5 =B6+C6 =B7+C7 =B8+C8 =B9+C9 =B10+C10 =B11+C11 9 -09 10 119 =D10 12 13 Simple Inte 14 Year Opening Balance 15 1 = 25000 16 2 =D15 173 =D16 18 4 =D17 195 =D18 206 =D19 =D20 22 8 =D21 239 =D22 24 25 Year Coumpound 26 1 26000 27040 28 3 28121.6 294 29246.464 30416.32256 316 31632.9754624 327 32898.294480896 34214.2262601318 34 9 35582.7953105371 35 Interest = 25000*4% = 25000*4% =25000*4% = 25000*4% =25000*4% = 25000*4% = 25000*4% =25000*4% = 25000*4% Closing Balance =B15+C15 =B16+C16 =B17+C17 =B18+C18 =B19+C19 =B20+C20 =B21+C21 =B22+C22 =B23+C23 21 7 27 2 Simple 26000 27000 28000 29000 30000 31000 32000 33000 34000 Difference =B26-C26 =B27-027 =B28-C28 =B29-C29 =B30-C30 =B31-C31 =B32-C32 =B33-C33 =B34-C34

the number of years it takes for the the difference of the TOTAL using Simple interest and TOTAL using compound interest (compounded annually) to reach more than $1000 is 8 Years

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