Question:
If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$4028
Solution And Explanation
Solution
Given,
Principal (P) = $3800
Rate of Simple Interest (SI) = 3%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $3800 × 3% × 2
= $3800 ×3/100 × 2
= 3800 × 3 × 2/100
= 11400 × 2/100
= 22800/100
= $228
Thus, Simple Interest = $228
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $3800 + $228
= $4028
Thus, Amount to be paid = $4028 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $3800
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 2 years
Thus, Amount (A)
= $3800 + ($3800 × 3% × 2)
= $3800 + ($3800 ×3/100 × 2)
= $3800 + (3800 × 3 × 2/100)
= $3800 + (11400 × 2/100)
= $3800 + (22800/100)
= $3800 + $228 = $4028
Thus, Amount (A) to be paid = $4028 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3800, the simple interest in 1 year
= 3/100 × 3800
= 3 × 3800/100
= 11400/100 = $114
Thus, simple interest for 1 year = $114
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $114 × 2 = $228
Thus, Simple Interest (SI) = $228
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3800 + $228
= $4028
Thus, Amount to be paid = $4028 Answer
Similar Questions
(1) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.
(2) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.
(3) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.
(5) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(6) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
(7) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(8) If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?