Question:
Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 7 years.
Correct Answer
$7680
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 4%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 7
= $6000 ×4/100 × 7
= 6000 × 4 × 7/100
= 24000 × 7/100
= 168000/100
= $1680
Thus, Simple Interest = $1680
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 + $1680
= $7680
Thus, Amount to be paid = $7680 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) = 4%
And, Time (t) = 7 years
Thus, Amount (A)
= $6000 + ($6000 × 4% × 7)
= $6000 + ($6000 ×4/100 × 7)
= $6000 + (6000 × 4 × 7/100)
= $6000 + (24000 × 7/100)
= $6000 + (168000/100)
= $6000 + $1680 = $7680
Thus, Amount (A) to be paid = $7680 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $6000, the simple interest in 1 year
= 4/100 × 6000
= 4 × 6000/100
= 24000/100 = $240
Thus, simple interest for 1 year = $240
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $240 × 7 = $1680
Thus, Simple Interest (SI) = $1680
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $1680
= $7680
Thus, Amount to be paid = $7680 Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(2) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?
(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 9% simple interest?
(4) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.
(6) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8791 to clear the loan, then find the time period of the loan.
(7) How much loan did Christopher borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6900 to clear it?
(8) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?
(9) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 6% simple interest?
(10) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.