Question:
Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 4 years.
Correct Answer
$4760
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 10%
Time (t) = 4 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) = $3400 × 10% × 4
= $3400 ×10/100 × 4
= 3400 × 10 × 4/100
= 34000 × 4/100
= 136000/100
= $1360
Thus, Simple Interest = $1360
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 = $3400 + $1360
= $4760
Thus, Amount to be paid = $4760 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 = $3400
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 4 years
Thus, Amount (A)
= $3400 + ($3400 × 10% × 4)
= $3400 + ($3400 ×10/100 × 4)
= $3400 + (3400 × 10 × 4/100)
= $3400 + (34000 × 4/100)
= $3400 + (136000/100)
= $3400 + $1360 = $4760
Thus, Amount (A) to be paid = $4760 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 $3400, the simple interest in 1 year
= 10/100 × 3400
= 10 × 3400/100
= 34000/100 = $340
Thus, simple interest for 1 year = $340
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $340 × 4 = $1360
Thus, Simple Interest (SI) = $1360
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $1360
= $4760
Thus, Amount to be paid = $4760 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 7 years.
(2) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
(3) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?
(4) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(5) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(6) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?
(7) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.
(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?
(9) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.
(10) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.