Question:
Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.
Correct Answer
$7440
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $6000 × 3% × 8
= $6000 ×3/100 × 8
= 6000 × 3 × 8/100
= 18000 × 8/100
= 144000/100
= $1440
Thus, Simple Interest = $1440
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 = $6000 + $1440
= $7440
Thus, Amount to be paid = $7440 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 = $6000
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $6000 + ($6000 × 3% × 8)
= $6000 + ($6000 ×3/100 × 8)
= $6000 + (6000 × 3 × 8/100)
= $6000 + (18000 × 8/100)
= $6000 + (144000/100)
= $6000 + $1440 = $7440
Thus, Amount (A) to be paid = $7440 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $6000, the simple interest in 1 year
= 3/100 × 6000
= 3 × 6000/100
= 18000/100 = $180
Thus, simple interest for 1 year = $180
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $180 × 8 = $1440
Thus, Simple Interest (SI) = $1440
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $1440
= $7440
Thus, Amount to be paid = $7440 Answer
Similar Questions
(1) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(2) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.
(3) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(4) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(5) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.
(6) If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?
(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 9% simple interest?
(9) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?
(10) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?