At what rate of simple interest will a sum of money amounts to 6 5 of itself in 2 years 6 months?

Saving

The power of compounding grows your savings faster

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The sooner you start to save, the more you'll earn with compound interest.

Compound interest is the interest you get on:

• the money you initially deposited, called the principal
• the interest you've already earned

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 interest

The 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:

• After five years, you'd have $11,616. You'd earn $1,616 in interest.
• After 10 years you'd have $13,494. You'd earn $3,494 in interest.
• After 20 years you'd have $18,208. You'd earn $8,208 in interest.

Compound interest formula

To 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 interest

To 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 has $12,834.
• Lorenzo has $12,500.

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.

Principal: The money which we deposit in or the lower from the bank or the money learned called the principal.

Rate of interest: The interest paid on $ 100 for one year is called the rate per cent per year or rate per cent per annum.

Time: The period of time for which the money is lent or invested.

Interest: Additional money paid by the borrowed to the lender for using the money is called interest.

Simple Interest: If the interest is calculated uniformly on the original principal throughout the lone period, it is called simple interest.

Amount: The total money paid back to the lender is called the amount.

Calculate Simple Interest

Formula to calculate Simple Interest?

If P denotes the principal ($), R denotes the rate (percentage p.a.) and T denotes time (years), then:-

S.I = (P × R × T)/100

R = (S.I × 100)/(P × T)

P = (S.I × 100)/(R × T)

T = (S.I × 100)/(P × R)

If the denotes the amount, then A = P + S.I

Note:

● When we calculated the time period between two dates, we do not could the day on which money is deposited but we count the day on which money is retuned.

● Time is always taken according to the per cent rat.

● For converting time in days into years, divide th number of days by 365 (for ordering or lap year.)

● For converting time in month into years, divide th number of month by 12 (for ordering or lap year.)

Examples to find or calculate simple interest when principal, rate and time are known

Calculate Simple Interest

Find the simple interest on:

(a) $ 900 for 3 years 4 months at 5% per annum. Find the amount also.

Solution:

R = 5% p.a.

T = 3 years 4 months = 40/12 years = 10/3 years Therefore, S.I = (P × R × T)/100 = (900 × 5 × 10)/(100 × 3) = $ 150

Amount = P + S.I = $ 900 + $ 150 = $ 1050

(b) $ 1000 for 6 months at 4% per annum. Find the amount also.

Solution:

R = 4% p.a.

T = 6 months = 6/12 years S.I = (P × R × T)/100 = (1000 × 4 × 1)/(100 × 2) = $ 20 Therefore, A = P + I = $( 1000 + 20) = $ 1020

(c) $ 5000 for 146 days at 15¹/₂% per annum.

Solution:

(d) $ 1200 from 9ᵗʰ April to 21ˢᵗ June at 10% per annum.

Solution:

= 73 days [April = 21, May = 31, Jun = 21, 73 days]

= 73/365 years

S.I = (1200 × 10 × 73)/(100 × 365) = $ 24

Examples to find or calculate Time when Principal, S.I and Rate are known

Calculate Simple Interest

1. In how much time dose $ 500 invested at the rate of 8% p.a. simple interest amounts to $ 580.

Solution:

Therefore S.I = A - P = $ (580 - 500) = $ 80

Therefore T = (100 × S.I)/(P × R) = (100 × 80)/(500 × 3) = 2 years

2. In how many years will a sum of $ 400 yield an interest of $ 132 at 11% per annum?

Solution:

Calculate Simple Interest

3. In how many years will a sum double itself at 8 % per annum?

Solution:

So , S.I. = A - P = 2P – P = P

T = (100 × S.I)/(P × R) = ( 100 × P)/(P × 8) = 25/2 = 121/2 years

Calculate Simple Interest

4. In how many years will simple interest on certain sum of money at 6 1/4% Per annum be 5/8 of itself?

Solution:

T = 10 years

Examples to find or calculate Rate per cent when Principal, S.I. and Time are known

1. Find at what rate of interest per annum will $ 600 amount to $ 708 in 3 years.

Solution:

Calculate Simple Interest

2. Simple interest on a certain sum is 36/25 of the sum. Find the Rate per cent and time if they are both numerically equal.

Solution:

Calculate Simple Interest

3. At what rate per cent per annum will $ 6000 produce $ 300 as S.I. in 1 years?

Solution:

4. At what rate per cent per annum will a sum triple itself in 12 years ?

Solution:

Examples to find or calculate Principal when Rate, Time and S.I. are known

Calculate Simple Interest

1. What sum will yield $ 144 as S.I. in 21/2 years at 16% per annum?

Solution:

2. A some amount to $ 2040 in 21/2 years at , P = ?

Solution:

51x = 2040 × 40 ---- x = (2040 × 40)/51 = $ 1600

Calculate Simple Interest

3. A certain sum amounts to $ 6500in 2 years and to $ 8750 in 5 years at S.I. Find the sum and rate per cent per annum.

Solution:

4. Divide $ 6500 in to two parts , such that if one part is lent out at 9% per annum and other at 10% per annum, the total yearly income is $ 605

Solution:

But given that total S.I.= $ 605

So, (6500 - x)/100 =605 -----65000 - x = 60500

----- 65000 – 60500 = x ---- x = $ 4500

Now, second part = 6500 – x = 6500 – 4500 = $ 2000

Hence, first part = $ 2000 and second part = $ 4500

5. When the rate of interest in a bank is increased from 9% to 10% per annum; A person deposits $ 500 more into his account. If the annual interest now Received by him is $ 150more then before, find his original deposit.

Solution:

Then, S.I. on $ x for 1 year at (10 - 9 )% = 1% per annum + S.I. on $ 500

For I year at 10% per annum = $ 15

----- ( x × 1 × 1)/100 + ( 500 × 10 × 1)/100 = 150

----- x/(100 ) + 50 = 150 ---- x/(100 ) + 150 – 50 ----- x/(100 ) + 100

----- x = 100 × 100 = $ 10,000

Therefore, the original deposit is $ 10,000.

Calculate Simple Interest

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What is Simple Interest?

Calculate Simple Interest

Practice Test on Simple Interest

● Simple Interest - Worksheets

Simple Interest Worksheet

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