Studying about compound interest we have known about the formulae used in compound interest. Also, we solved few examples based on them. Now, under this topic we’ll solve few more questions based on the formulae used in the compound interest. Lets first have a recap about the formulae we came across:
Case 1: When the interest is compounded yearly:
A = \(P(1+\frac{R}{100})^{T}\)
Case 2: When the interest is compounded half yearly:
A = \(P(1+\frac{\frac{R}{2}}{100})^{2T}\)
Case 3: When the interest is compounded quarterly:
A = \(P(1+\frac{\frac{R}{4}}{100})^{4T}\)
Case 4: When the time is in fraction of a year, say \(2^{\frac{1}{5}}\), then:
A = \(P(1+\frac{R}{100})^{2}(1+\frac{\frac{R}{5}}{100})\)
Case 5: If the rate of interest in 1st year, 2nd year, 3rd year,…, nth year are R1%, R2%, R3%,…, Rn% respectively. Then,
A = \(P(1+\frac{R_{1}}{100})(1+\frac{R_{2}}{100})(1+\frac{R_{3}}{100})...(1+\frac{R_{n}}{100})\)
Case 6: Present worth of Rs x due ‘n’ years hence is given by:
Present worth = \(\frac{1}{1+\frac{R}{100}}\)
where symbols have their usual meanings.
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 try to solve below given questions based upon these formulae:
1) A man borrows $20,000 from a bank at the interest rate of 6% per annum compounded annually. Calculate the amount that he needs to pay back the bank after 3 years. Also find the interest charged by the bank on the man.
2) Rishabh takes a loan of $25,00,000 from the bank at the interest rate of 10% per annum compounded annually for 5 years. Calculate the amount that he has to pay the bank after this tenure of time. Also, calculate the interest charged by the bank on this sum of money.
3) A man borrows an amount of $45,000 from a bank at the interest rate of 7% per annum compounded semi annually for 2 years. Calculate the amount that man needs to return to the bank after this period of time. Also, find the interest charged by the bank.
4) A bank lends a sum of $25,000 to a man at an interest rate of 10% per annum compounded quarterly. Calculate the amount that the man needs to pay to the bank after a tenure of 3 years. Also calculate the interest charged by the bank on this amount.
5) Rajeev took a loan of $10,00,000 from a bank at an interest of 7% per annum compounded quarterly for 5 years. Calculate the amount he pays to the bank after this period of time. Also, calculate the interest charged by the bank on this sum.
6) Three consecutive rates of interest are applied on a sum of $25,000. The rates of interest are 5%, 10% and 12% for three years. Calculate the amount one needs to pay to the bank after three years of tenure. Also find the interest charged by the bank.
7) If rates of 6%, 8%, 10% and 15% are rates of interest charged by a bank 4 consecutive years on a sum of Rs2,00,000. Calculate the amount one needs to pay to the bank for the sum. Also, calculate the interest charged by the bank on this sum.
Solutions:
1) Amount = $23,820.32
Interest = $3,820.32
2) Amount = $40,26,275
Interest = $15,26,275
3) Amount = $51,638.53
Interest = $6,638.53
4) Amount = $33,622.22
Interest = $8,622.22
5) Amount = $14,14,778.19
Interest = $4,14,778.19
6) Amount = $32,340
Interest = $7,340
7) Amount = $2,89,634.4
Interest = $89,634.4
9th Grade Math
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