Question:
Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.
Correct Answer
$9780
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 7%
Time (t) = 9 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% × 9
= $6000 ×7/100 × 9
= 6000 × 7 × 9/100
= 42000 × 9/100
= 378000/100
= $3780
Thus, Simple Interest = $3780
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 + $3780
= $9780
Thus, Amount to be paid = $9780 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) = 9 years
Thus, Amount (A)
= $6000 + ($6000 × 7% × 9)
= $6000 + ($6000 ×7/100 × 9)
= $6000 + (6000 × 7 × 9/100)
= $6000 + (42000 × 9/100)
= $6000 + (378000/100)
= $6000 + $3780 = $9780
Thus, Amount (A) to be paid = $9780 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 9 years
= Simple interest for 1 year × 9
= $420 × 9 = $3780
Thus, Simple Interest (SI) = $3780
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $3780
= $9780
Thus, Amount to be paid = $9780 Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.
(2) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.
(3) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?
(4) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 6% simple interest?
(5) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(6) What amount does James have to pay after 6 years if he takes a loan of $3000 at 3% simple interest?
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 4 years.
(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 5% simple interest?
(9) What amount does John have to pay after 6 years if he takes a loan of $3200 at 2% simple interest?
(10) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.