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

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

Answers ( )

    0
    2021-09-18T16:22:39+00:00

    Answer:

    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

    0
    2021-09-18T16:22:40+00:00

    Answer

    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

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