Question:
What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?
Correct Answer
$4402
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 7%
Time (t) = 6 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) = $3100 × 7% × 6
= $3100 ×7/100 × 6
= 3100 × 7 × 6/100
= 21700 × 6/100
= 130200/100
= $1302
Thus, Simple Interest = $1302
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 = $3100 + $1302
= $4402
Thus, Amount to be paid = $4402 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 = $3100
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 6 years
Thus, Amount (A)
= $3100 + ($3100 × 7% × 6)
= $3100 + ($3100 ×7/100 × 6)
= $3100 + (3100 × 7 × 6/100)
= $3100 + (21700 × 6/100)
= $3100 + (130200/100)
= $3100 + $1302 = $4402
Thus, Amount (A) to be paid = $4402 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 $3100, the simple interest in 1 year
= 7/100 × 3100
= 7 × 3100/100
= 21700/100 = $217
Thus, simple interest for 1 year = $217
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $217 × 6 = $1302
Thus, Simple Interest (SI) = $1302
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $1302
= $4402
Thus, Amount to be paid = $4402 Answer
Similar Questions
(1) How much loan did Ashley borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7205 to clear it?
(2) Michelle had to pay $5247 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 John have to pay after 5 years if he takes a loan of $3200 at 10% simple interest?
(4) If Susan paid $4380 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(6) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
(7) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(8) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?
(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.
(10) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 8 years.