Interest

Concept

The extra amount paid for borrowed amount which is paid in a pre-determined rate and for a specific period is called interest. This pre-determined rate is called interest rate and the borrowed or investment amount is called principal. The amount of interest is paid as an additional amount with borrowed or invested amount.

There are two types of interest:

Simple Interest
Compound Interest

Simple Interest: When interest is computed only on the initial principal amount, it is called simple interest. If $100.00 is invested @10%, then interest for three years will be $ 30.00.

Compound Interest: When interest is calculated on accumulated value of principal and interest, it is called compound interest. compounded interest can be calculated daily, monthly, half-yearly, quarterly or even annually. If $100.00 is invested @10%, then interest for three years will be $33.10 provided that interest is calculated per annum basis. In this types of question Interest rate, principal, Interest amount and time are provided except any one of the aforesaid data which is asked to find out.

Tips to solve problems on percentage:

To calculate simple interest, I = pnr; where, I = Total interest earned, p = Total principal or initial investment, n = No. of year or time & r = Rate of interest.
To calculate compounded amount, C = p(1+nr), or C = P(1+r)^n; where, C= Cumulative amount (principal+interest), P= Principal, n= Time, r= rate of interest

Q. David invests $5000 in a bank account that pays 4% simple interest per year. How much interest will he earn in 5 years?

A) $200

B) $800

C) $1000

To find the simple interest, we use the formula I=P×R×T, where I=interest, P=principal, R=rate, and T=time. Plugging in the given values, we get I=5000×0.04×5=1000 Therefore, David will earn $1000 in interest in 5 years.

D) $1200

Discuss

Q. Sam invests $2000 in a bank account that pays 3% simple interest per year for the first two years and then switches to 4% compound interest per year for the next two years. How much money will he have in his account after four years?

A) $2332.32

B) $2345.60

C) $2356.48

To find the total amount, we need to calculate the simple interest for the first two years and then add it to the principal to get the new balance. Then, we need to calculate the compound interest for the next two years using the new balance as the principal. For the simple interest, we use the formula I=P×R×T and get, I=2000×0.03×2=120. Adding this to the principal, we get 2000+120=2120. This is the new balance after two years. For the compound interest, we use the formula A=P×(1+R)T and get A=2120×(1+0.04)2=2356.48 This is the final amount after four years.

D) $2368.00

Discuss

Q. Kelly deposits $1000 in a savings account that pays 2% compound interest per year. How long will it take for her money to double?

A) 35 years

B) 36 years

To find how long it will take for her money to double, we need to solve for T. In the equation A=P×(1+R)T, where A= final amount, P=principal, R= rate, and T=time. Since we want her money to double, we set A=2P and get 2P=P×(1+R)T. Dividing both sides by P and taking the natural logarithm of both sides, we get (2)=T×ln(1+R). Solving for T, we get T=ln(1+R)ln(2). Plugging in the given values, we get T=ln(1+0.02)ln(2)≈35.0028. Rounding up to the nearest whole number, we get T=36 Therefore, it will take Kelly 36 years for her money to double.

C) 37 years

D) 38 years

Discuss

Q. Ryan invests $4000 in a bond that pays 5% simple interest per year. He also invests $6000 in a stock that pays 8% compound interest per year. How much more interest will he earn from the stock than from the bond after 10 years?

A) $2400

B) $2800

C) $3200

D) $3600

To find the difference in interest, we need to calculate the interest earned from each investment and then subtract them. For the bond, we use the formula I=P×R×T and getI=4000×0.05×10=2000. For the stock, we use the formula A=P×(1+R)T and get A=6000×(1+0.08)10=12986.40. The interest earned from the stock is the difference between the final amount and the principal, which is 12986.40−6000=6986.40 . The difference in interest is then 6986.40−2000=4986.40 . Rounding down to the nearest hundred, we getD=3600. Therefore, Ryan will earn $3600 more interest from the stock than from the bond after 10 years

Discuss

Interest

Concept

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