## 8) Arif took a loan of 80,000 from a bank. If the rate of interest is 10% per annum, find the difference inamounts he would

Question

8) Arif took a loan of 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in
amounts he would be paying after 11/2 years if the interest is compounded annually.​

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1 month 2021-09-18T16:21:03+00:00 2 Answers 0 views 0

42984

Step-by-step explanation:

Principal = 80000

Rate = 10

Time period = 5 complete yrs. and 1 half year

Amount = P (100+r/100)^T

= 80000 (100+10/100)^5 × (100+5/100)^1

= 80000 (110/100)^5 × (105/100)

= 80000 (11/10)(11/10)(11/10)(11/10)(11/10)(105/100)

= 8 (121)(121)(105/100)

= 2 (121)(121)(105/25)

= 242(121)(21/5)

= 29282(21/5)

= 122984.4

= 122984

Difference = 122984 – 80000

= 42984

1) Compounded Annually :

P=Rs.80000

R=10% p.a.

T=1 1/2    years ⟹n=1+  2
1

Amount for 1st year.

A=P[1+  R/100  ]  n

=Rs.80000[1+  10/100
]=Rs.88000

SI on Rs. 88000 for next 1/2 year

=Rs.88000×  10/100  ​
× 1/2   =Rs.4400

Therefore, Amount = Rs.88000+Rs.4400 = 92400Rs.

2) Compounded half yearly :

P=Rs.80000

R=10% p.a.=5% per half year

T=1  1
/2 years ⟹n=3

A=Rs.80000[1+ 5/100   ]  3

A=Rs.92610

Thus, the difference between the two amounts = Rs.92610−Rs.92400 =Rs.210