Question:
What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?
Correct Answer
$5600
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 10%
Time (t) = 6 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) = $3500 × 10% × 6
= $3500 ×10/100 × 6
= 3500 × 10 × 6/100
= 35000 × 6/100
= 210000/100
= $2100
Thus, Simple Interest = $2100
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 = $3500 + $2100
= $5600
Thus, Amount to be paid = $5600 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 = $3500
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 6 years
Thus, Amount (A)
= $3500 + ($3500 × 10% × 6)
= $3500 + ($3500 ×10/100 × 6)
= $3500 + (3500 × 10 × 6/100)
= $3500 + (35000 × 6/100)
= $3500 + (210000/100)
= $3500 + $2100 = $5600
Thus, Amount (A) to be paid = $5600 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 $3500, the simple interest in 1 year
= 10/100 × 3500
= 10 × 3500/100
= 35000/100 = $350
Thus, simple interest for 1 year = $350
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $350 × 6 = $2100
Thus, Simple Interest (SI) = $2100
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $2100
= $5600
Thus, Amount to be paid = $5600 Answer
Similar Questions
(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 8 years.
(2) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 2% simple interest?
(4) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 3 years.
(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(7) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
(8) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(9) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(10) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?