If the principal be Rs. P and the annual rate of interest be r1% in the 1st year , r2% in the 2nd year , then write the amount after n years
Answers
Answer:
We have learnt about compound interest in previous topics of this chapter. Under this topic, we’ll be dealing from formulae that are useful in calculating compound interest in different cases. Following are the cases and formulae used in them to calculate the amount payable at the principal sum......
If ‘P’ is the principal sum, i.e., amount taken as loan.
‘R’ is the rate percent which the bank/ lender is charging at the principal amount.
‘T’ is the time duration in which you have to repay the amount,
And ‘A’ will be the amount to be paid in following cases using following formulae:
Case 1: When the interest is compounded yearly:
A = P(1+R100)T
Case 2: When the interest is compounded half yearly:
A = P(1+R2100)2T
Case 3: When the interest is compounded quarterly:
A = P(1+R4100)4T
Case 4: When the time is in fraction of a year, say \{2^{\frac{1}{5}}\), then:
A = P(1+R100)2(1+R5100)
Case 5: If the rate of interest in 1st year, 2nd year, 3rd year,…, nth year are R1%, R2%, R3%,…, Rn% respectively. Then,
A = P(1+R1100)(1+R2100)(1+R3100)...(1+Rn100)
Case 6: Present worth of Rs x due ‘n’ years hence is given by:
Present worth = 11+R100
A fact that we all know very well is that interest is the difference between amount and principal sum, i.e.,
Interest = Amount – Principal
Now let us solve some problems based upon these formulae:
1. A man borrowed $20,000 from a bank on an interest of 10% p.a. compounded annually for 3 years. Calculate the compound amount and interest.
Solution:
R = 10%
P = $20,000
T = 3 years
We know that, A = P(1+R100)T
A = 20,000(1+10100)3
A = 20,000(110100)3
A = 20,000(1110)3
A = 20,000(13311000)
A = 26,620
So, amount = $26,620
Interest = amount – principal amount
= $26,620 – $20,000
= $6,620
Step-by-step explanation:
Solution:
R = 10%
P = $20,000
T = 3 years
We know that, A = P(1+R100)T
A = 20,000(1+10100)3
A = 20,000(110100)3
A = 20,000(1110)3
A = 20,000(13311000)
A = 26,620
So, amount = $26,620
Interest = amount – principal amount
= $26,620 – $20,000
= $6,620