Amount without compounding
When the interest is paid out every year, each year earns the same.
₹6000 for 3 years
You put ₹6000 in an FD at 10% p.a. for 3 years. The bank pays out the interest every year, and gives back the ₹6000 at the end.
How much do you receive in total?
What this lesson covers
The idea
Without compounding the principal p stays the same every term, so the interest each term is p × r and the total amount after t terms is p + prt = p(1 + rt), r being the rate per term.
₹6000 for 3 years
You put ₹6000 in an FD at 10% p.a. for 3 years. The bank pays out the interest every year, and gives back the ₹6000 at the end.
How much do you receive in total?
- ₹7,800
- ₹7,986
- ₹6,600
Stack the years
The principal never changes, so each year adds an equal block of interest. Choose the years and the rate. Reach the amounts in the goal.
The same interest every year
Without compounding the principal p stays the same every term, so the interest each term is p × r, and the total amount after t terms is p + prt = p(1 + rt), r being the rate per term.
₹6000 at 10% for 3 years: Interest each year: 0.10 × 6000 = ₹600 In 3 years: 3 × 600 = ₹1800 Total amount: 6000 + 1800 = ₹7800
As a formula: 6000 × (1 + 0.1 × 3) = 6000 × 1.3 = ₹7800 The amount is 130% of the principal, a gain of 30% over 3 years.
Notes
Without compounding the principal p stays the same every term, so the interest each term is p × r, and the total amount after t terms is p + prt = p(1 + rt), r being the rate per term.
Check yourself
₹5000 is put in an FD at 8% p.a. for 2 years, and the interest is paid out every year. What is the total amount received (in ₹)?
Answer: 5800
Interest each year: 0.08 × 5000 = ₹400 In 2 years: 2 × 400 = ₹800 Amount: 5000 + 800 = ₹5800
Use p(1 + rt) to find the amount for a principal of ₹2000 at 5% p.a. for 4 years (in ₹).
Answer: 2400
1 + 0.05 × 4 = 1.2 Amount: 2000 × 1.2 = ₹2400
₹4000 is put in an FD at 10% p.a. for 3 years without compounding. What is the interest in the 3rd year?
Interest of ₹1500 is paid in all on a principal of ₹5000 over 5 years, without compounding. What is the rate of interest per annum?
Answer: 6 %
Interest each year: 1500 ÷ 5 = ₹300 Rate: 300/5000 × 100 = 6%
- ₹400, the same as every other year — correct. Yes! Without compounding the principal stays ₹4000, so every year earns 10% of 4000 = ₹400.
- More than ₹400, because the money has grown. That is compounding. Here the interest is paid out, so the principal stays ₹4000 and each year earns the same ₹400.
- ₹1200, the interest of all three years. ₹1200 is the total for 3 years. Each year earns ₹400.