Question:
Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.
Correct Answer
$4658.5
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 7%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $3850 × 7% × 3
= $3850 ×7/100 × 3
= 3850 × 7 × 3/100
= 26950 × 3/100
= 80850/100
= $808.5
Thus, Simple Interest = $808.5
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 = $3850 + $808.5
= $4658.5
Thus, Amount to be paid = $4658.5 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 = $3850
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 3 years
Thus, Amount (A)
= $3850 + ($3850 × 7% × 3)
= $3850 + ($3850 ×7/100 × 3)
= $3850 + (3850 × 7 × 3/100)
= $3850 + (26950 × 3/100)
= $3850 + (80850/100)
= $3850 + $808.5 = $4658.5
Thus, Amount (A) to be paid = $4658.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3850, the simple interest in 1 year
= 7/100 × 3850
= 7 × 3850/100
= 26950/100 = $269.5
Thus, simple interest for 1 year = $269.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $269.5 × 3 = $808.5
Thus, Simple Interest (SI) = $808.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $808.5
= $4658.5
Thus, Amount to be paid = $4658.5 Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
(2) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.
(3) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.
(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 7% simple interest?
(5) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.
(6) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?
(7) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?
(8) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 10% simple interest?
(9) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.