Question

find the difference between compound interest and simple interest on a sum of rupees 64000 @ 20% per annum compounded semi annually for one 1/ 2 years​

Answer 1

Answer:

Rs 1984

Step-by-step explanation:

Simple Interest = $\frac {principle * rate of interest * time }{100}$

Simple Interest = $\frac { 64000 * 20 * 1.5 }{100}$

Simple Interest = 640 × 30

Simple Interest = 19200 Rs

Compound interest = $(principle * ( 1 + \frac {r} {100n} )^{(nt)} ) - principle$

Compound interest = $(64000 * ( 1 + \frac {20} {100 * 2} )^{(2 * 1.5)} ) - 64000$

Compound interest = $(64000 * ( 1 + 0.1} )^3 ) - 64000$

Compound interest = $(64000 * ( 1.1} )^3 ) - 64000$

Compound interest = (64000 × 1.331) - 64000

Compound interest = (64000 )× (1.331- 1)

Compound interest = (64000 )× (0.331) = 21184

Difference between compound and simple interest = 21184 - 19200

= 1984

Answer 2

Principal (P)=₹64000

Time (T)=one whole1/2 years=(3/2×2) half years=3 half years

Rate of interest (R)=20% p.a.=(20/2)% per half year=10% per half year

So, Compound Interest (CI)=Amount-Principal

=P(1+R/100)^n-P

=64000(1+10/100)³-64000

=64000(1+1/10)³-64000

=64000×(11/10)³-64000

=64000×11/10×11/10×11/10-64000

=85184-64000

=₹21184

So, CI=₹21184

Now, Principal (P)=₹64000

Time (T)=3/2 years

Rate of interest (R)=20% p.a.

So, Simple Interest=PRT/100

=64000×20×3/100×2

=₹19200

So, SI=₹19200

So, the difference between the compound interest and the simple interest=CI-SI=₹(21184-19200)=₹1984