Assignment on Compound interest / loan

Assignment on compound interest

Created by: John Vagmi edu.com

Price $4

Total number of questions 4

Standard -Moderate to hard

Time: 30min

Solution: Yes

sample question: What is the difference between the compound interests on Rs. 5000 for 1 ½ year at 4% per annum compounded yearly and half-yearly?

Solution:

Given,

P = Rs. 5000

R = 4%

Time (n) = 1 ½ years

When the interest is compounded yearly,

A = P[1 + (R/100)]n

= Rs. 5000 [1 + (4/100)] [1 + (1/2 × 4/100)]

= Rs. 5000 [1 + (1/25)] [1 + (1/50)]

= Rs. 5000 [(25 + 1)/25] [(50 + 1)/50]

= Rs. 5000 × (26/25) × (51/50)

= Rs. 5304

CI = A – P = Rs. 5304 – Rs. 5000 = Rs. 304

When the interest is compounded half-yearly,

n = 1 ½ years = 3 half-years

A = P[1 + (R/200)]2n

Here, 2n = 3

A = Rs. 5000 [1 + (4/200)]3

= Rs. 5000 [1 + (1/50)]3

= Rs. 5000 [(50 + 1)/50]3

= Rs. 5000 × (51/50) × (51/50) × (51/50)

= Rs. 5306.04

CI = A – P = Rs. 5306.04 – Rs. 5000 = Rs. 306.04

Difference between compound interest = Rs. 306.04 – Rs. 304 = Rs. 2.04