Question:
Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 3 years.
Correct Answer
$3965
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (SI) = 10%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $3050 × 10% × 3
= $3050 ×10/100 × 3
= 3050 × 10 × 3/100
= 30500 × 3/100
= 91500/100
= $915
Thus, Simple Interest = $915
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 = $3050 + $915
= $3965
Thus, Amount to be paid = $3965 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 = $3050
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 3 years
Thus, Amount (A)
= $3050 + ($3050 × 10% × 3)
= $3050 + ($3050 ×10/100 × 3)
= $3050 + (3050 × 10 × 3/100)
= $3050 + (30500 × 3/100)
= $3050 + (91500/100)
= $3050 + $915 = $3965
Thus, Amount (A) to be paid = $3965 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3050, the simple interest in 1 year
= 10/100 × 3050
= 10 × 3050/100
= 30500/100 = $305
Thus, simple interest for 1 year = $305
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $305 × 3 = $915
Thus, Simple Interest (SI) = $915
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $915
= $3965
Thus, Amount to be paid = $3965 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(2) 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?
(3) What amount does William have to pay after 6 years if he takes a loan of $3500 at 9% simple interest?
(4) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 7% simple interest.
(6) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 4 years.
(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 3 years.
(9) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 7% simple interest?
(10) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.