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The power of compounding grows your savings faster 3 minutes
The sooner you start to save, the more you'll earn with compound interest. Compound interest is the interest you get on:
For example, if you have a savings account, you'll earn interest on your initial savings and on the interest you've already earned. You get interest on your interest. This is different to simple interest. Simple interest is paid only on the principal at the end of the period. A term deposit usually earns simple interest. Save more with compound interestThe power of compounding helps you to save more money. The longer you save, the more interest you earn. So start as soon as you can and save regularly. You'll earn a lot more than if you try to catch up later. For example, if you put $10,000 into a savings account with 3% interest compounded monthly:
Compound interest formulaTo calculate compound interest, use the formula: A = P x (1 + r)n A = ending balanceP = starting balance (or principal)r = interest rate per period as a decimal (for example, 2% becomes 0.02) n = the number of time periods How to calculate compound interestTo calculate how much $2,000 will earn over two years at an interest rate of 5% per year, compounded monthly: 1. Divide the annual interest rate of 5% by 12 (as interest compounds monthly) = 0.0042 2. Calculate the number of time periods (n) in months you'll be earning interest for (2 years x 12 months per year) = 24 3. Use the compound interest formula A = $2,000 x (1+ 0.0042)24A = $2,000 x 1.106 A = $2,211.64
Lorenzo and Sophia compare the compounding effect
Lorenzo and Sophia both decide to invest $10,000 at a 5% interest rate for five years. Sophia earns interest monthly, and Lorenzo earns interest at the end of the five-year term. After five years:
Sophia and Lorenzo both started with the same amount. But Sophia gets $334 more interest than Lorenzo because of the compounding effect. Because Sophia is paid interest each month, the following month she earns interest on interest.
10 Questions 10 Marks 10 Mins
Alternate MethodRate of interest half yearly = 5/2 = 2.5% Equivalent rate of interest for one year = 2.5 + 2.5 + (2.5 × 2.5)/100 ⇒ 5.0625% Compound interest = 4000 × 5.0625/100 = Rs. 202.5 Rate of interest quarterly = 40/4 = 10% Equivalent rate of interest = [(11/10 × 11/10 × 11/10 × 11/10) - 1] = 46.41% Compound interest = 2000 × 46.41/100 = Rs. 928.2 Total interest = 202.5 + 928.2 = Rs. 1130.70 Traditional method: Given Case-1 Principal = Rs. 4000 Rate = 5% Time = 1 year Interest compounded half yearly. Case-2 Principal = Rs. 2000 Rate = 40% Time = 1 year Interest compounded quaterly. Formula: A = P (1 + r/100)t Calculation: For case-1 r = 5/2% = 2.5% Time = 2 According to the formula A = 4000 × (102.5/100) × (102.5/100) ⇒ A = 4,202.5 CI = 4,202,5 - 4,000 = 202.5 For case-2 r = 40/4 = 10% Time = 4 According to the formula A = 2000 × (110/100) × (110/100) × (110/100) × (110/100) ⇒ A = 2,928.2 CI = 2,928.2 - 2,000 = Rs. 928.2 Total interest = 202.5 + 928.2 = Rs. 1,130.70 ∴ The total interest is Rs. 1,130.70. India’s #1 Learning Platform Start Complete Exam Preparation
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Calculate the amount and compound interest on: (a) Rs 10,800 for 3 years at 121/2 % per annum compounded annually. (b) Rs 18,000 for 21/2 years at 10% per annum compounded annually. (c) Rs 62,500 for 11/2 years at 8% per annum compounded half yearly (d) Rs 8,000 for 1 year at 9% per annum compounded half yearly. (You could use the year by year calculation using SI formula to verify.) (e) Rs 10,000 for 1 year at 8% per annum compounded half yearly.
Answer Hint: We need the formula for finding the amount. We use the formula \[A = P{ \left[ {1 + \dfrac{r}{{100}}} \right] ^n} \] where, \[A \] is the amount, \[P \] is principal amount, \[r \] is the rate percent yearly (or every fixed period) and \[n \] is the number of years (or terms of the fixed period). Since all the values are given, substituting in the above formula we get the required amount. Complete step-by-step answer: List out the given data, that isRate per annum, \[r = 5 \] Principle amount, \[P = 2400 \] Number of years, \[n = 2 \] The amount to be paid in case of compound interest is \[A = ? \] We know the formula, \[A = P{ \left[ {1 + \dfrac{r}{{100}}} \right] ^n} \] Substituting we get, \[ \Rightarrow A = 2400{ \left[ {1 + \dfrac{5}{{100}}} \right] ^2} \] Taking L.C.M. in bracket and simplify, we get: \[ \Rightarrow A = 2400{ \left[ { \dfrac{{105}}{{100}}} \right] ^2} \] Since square is there in the bracket, simplify it, we get: \[ \Rightarrow A = 2400{ \left[ { \dfrac{{21}}{{20}}} \right] ^2} \] Removing square, we get: \[ \Rightarrow A = 2400 \left[ { \dfrac{{21 \times 21}}{{20 \times 20}}} \right] \] Simply separating the numerator and denominator terms, \[ \Rightarrow A = \dfrac{{2400 \times 21 \times 21}}{{400}} \] Simple division, we get: \[ \Rightarrow A = 6 \times 21 \times 21 \] Multiplying we get, \[ \Rightarrow A = 2646 \] .Hence the required amount is 2646 rupees.That is, the amount Rs. 2646 to be paid at the end of 2 years on Rs. 2400 at 5% per annum compounded annually.So, the correct answer is “2646”. Note: If they ask for an amount to be paid in three year, just put n=3 and follow the same procedure. Students need to remember the formula so that you can solve the problem for different years, different rates of interest and as well as for different principal amounts. Carefully substitute the values. Principal amount is the money that you originally agreed to pay back. |
Find the amount to be paid at the end of 2 years on rs 4000 at 5 per annum compounded annually
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