Question

Investigate the difference between compounding annually and simple interest

Answer 1

Step-by-step explanation:

Simple interest formula

$A = P (1 + rt)$

Compound interest formula

$A = P(1 + \frac{r}{n})^{nt}$

a.

$A = 5000 (1 + 0.025*1)\\A=5000(1.025)\\A=5125$

Simple interest is $125

b

. $A = 5000 (1 + \frac{0.025}{1})^{1*1} \\A=5000(1.025)\\A= 5125$

Compound interest is $125

c. the result for both a and b are the same

d.

$A = 5000 (1 + 0.025*3) \\A=5000(1.075) \\A=5375$

the simple interest is $375

e

. $A = 5000 (1 + \frac{0.025}{1})^{1*3}] \\A=5000(1.025)^3 \\A=5000(1.077)\\A= 5385$

the compound interest is $385

f. the result compared, compound interest is $10 more than simple interest

g.

$A = 5000 (1 + 0.02*6) \\A=5000(1.12) \\A=5600$

the simple interest is $600

h.

$A = 5000 (1 + \frac{0.02}{1})^{1*6}] \\A=5000(1.12)^6 \\A=5000(1.9738) \\A= 9869$

the compound interest is $4869

i. the result from g and h, h is over 8 times bigger than g.

j. interest compound annually is not the same as simple interest, only for the case of a and b seeing that it is for 1 year. but for 2years and above there is difference as seen in c to h