Question:
Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 4 years.
Correct Answer
$4560
Solution And Explanation
Solution
Given,
Principal (P) = $3800
Rate of Simple Interest (SI) = 5%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 4
= $3800 ×5/100 × 4
= 3800 × 5 × 4/100
= 19000 × 4/100
= 76000/100
= $760
Thus, Simple Interest = $760
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 + $760
= $4560
Thus, Amount to be paid = $4560 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) = 5%
And, Time (t) = 4 years
Thus, Amount (A)
= $3800 + ($3800 × 5% × 4)
= $3800 + ($3800 ×5/100 × 4)
= $3800 + (3800 × 5 × 4/100)
= $3800 + (19000 × 4/100)
= $3800 + (76000/100)
= $3800 + $760 = $4560
Thus, Amount (A) to be paid = $4560 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3800, the simple interest in 1 year
= 5/100 × 3800
= 5 × 3800/100
= 19000/100 = $190
Thus, simple interest for 1 year = $190
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $190 × 4 = $760
Thus, Simple Interest (SI) = $760
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3800 + $760
= $4560
Thus, Amount to be paid = $4560 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.
(2) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.
(4) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.
(6) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.
(8) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 7 years.
(10) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.