1. A man lends 12,500 at 12% for the first year, at 15% for the second year and at 18% for the third year. If the rates of interest are compounded yearly; find the difference between the C.I. of the first year and the compound interest for the third year.
Answers
The difference between the C. I. of the first year and the compound interest for the third year is $ 1,398
Step-by-step explanation:
Consider the given data
A man lends rupees 12,500 at 12% for the first year, at 15%for second year and at 18%for the third year. The rates of interest are compounded yearly.
We will first find the amount at the end of every year.
Using formula for compound interest
A=P(1+r)^nA=P(1+r)
n
Where, A is amount
P is initial amount
r is rate of interest
n is time
And interest = Amount - Principal
For year 1
P = $ 12,500
r = 12% = 0.12
A=12500(1+0.12)^1A=12500(1+0.12)
1
Thus, A = $ 14,000
Interest for year 1 = 14,000 - 12,500 = $ 1,500
For year 2
P = $ 14,000
r = 15% = 0.15
A=14000(1+0.15)^1A=14000(1+0.15)
1
Thus, A = $ 16,100
Interest for year 2 = 16,100 - 14,000 = $ 2,100
For year 3
P = $ 16,100
r = 18% = 0.18
A=16100(1+0.18)^1A=16100(1+0.18)
1
Thus, A = $ 18,998
Interest for year 3 = 18,998 - 16,100 = $ 2,898
Thus, The difference between the C. I. of the first year and the compound interest for the third year is 2,898 - 1,500 = 1,398