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 1½ years if the interest is –
a) Compound Annually
b) Compounded half yearly. to
Answers
Answer:
compounded half yearly to
Given :-
• Arif took a loan of 80,000 from bank
• Rate of interest is 10% per annum
• Time period = 1½ years
Solution :-
a) Here,
Principal = Rs 80,000
Rate = 10% p.a
Time = 1½
Time = 1 + 1/2 years
Firstly, We will find the amount Compounded annually for 1 year
As we know that,
A = P ( 1 + R/100 )^n
Put the required values in the given formula,
A = 80000 ( 1 + 10/100 )^1
A = 80000( 100 + 10 / 100 )^1
A = 80000 * 110/100
A = 88000
Now,
Amount = Principal + SI
Put the required values,
88000 = 80000 + SI
SI = 88000 - 80000
SI = Rs 8000
Thus,
Interest for 1 year = Rs8000
Amount for 1 year = Rs88000
Now,
SI for next 1/2 year
Principal = Amount in previous year
Rate = 10% p. a
Time = 1/2 year
By using formula to calculate SI
SI = P * R * T / 100
SI = 88000 * 10 * ½ / 100
SI = 88000 * 10 * 1 / 100 * 2
SI = 880 * 5
SI = Rs 4400
Therefore,
SI for next year = Rs 4400
Now,
Total SI for 1½ years = 8000 + 4400 = 12400
Thus,
Amount = Principal + SI
Amount = 88000 + 12400
Amount = 92400
Hence, Amount = Rs 92400
Solution 2 :-
Here ,
We have to calculate Compound halfyearly
Therefore,
Principal = 80000
Rate = 10/2 = 5%
[ Compounded half yearly ]
Time = 1½ = 3/2 * 2 = 3 years
[ Compounded half yearly ]
Now,
As we know that,
A = P ( 1 + R/100 )^n
Put the required values,
A = 80000( 1 + 5/100 )^3
A = 80000( 1 + 1/20)^3
A = 80000 ( 21/20)^3
A = 80000 * 21/20 *21/20 *21/20
A = 80000 * 441/400 * 21 / 20
A = 200 * 441 * 21 /20
A = 10 * 441 * 21
A = 210 * 441
A = 92610
Now,
We have to calculate difference between amounts .
Therefore,
= 92610 - 92400
= 210