Question:
Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.
Correct Answer
$8940
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 7%
Time (t) = 7 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) = $6000 × 7% × 7
= $6000 ×7/100 × 7
= 6000 × 7 × 7/100
= 42000 × 7/100
= 294000/100
= $2940
Thus, Simple Interest = $2940
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 + $2940
= $8940
Thus, Amount to be paid = $8940 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) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $6000 + ($6000 × 7% × 7)
= $6000 + ($6000 ×7/100 × 7)
= $6000 + (6000 × 7 × 7/100)
= $6000 + (42000 × 7/100)
= $6000 + (294000/100)
= $6000 + $2940 = $8940
Thus, Amount (A) to be paid = $8940 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 $6000, the simple interest in 1 year
= 7/100 × 6000
= 7 × 6000/100
= 42000/100 = $420
Thus, simple interest for 1 year = $420
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $420 × 7 = $2940
Thus, Simple Interest (SI) = $2940
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $2940
= $8940
Thus, Amount to be paid = $8940 Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.
(3) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?
(4) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(5) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 5% simple interest?
(6) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?
(7) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 8 years.
(8) 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.
(9) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 6% simple interest?
(10) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.