Question:
Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.
Correct Answer
$10200
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 7%
Time (t) = 10 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% × 10
= $6000 ×7/100 × 10
= 6000 × 7 × 10/100
= 42000 × 10/100
= 420000/100
= $4200
Thus, Simple Interest = $4200
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 + $4200
= $10200
Thus, Amount to be paid = $10200 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) = 10 years
Thus, Amount (A)
= $6000 + ($6000 × 7% × 10)
= $6000 + ($6000 ×7/100 × 10)
= $6000 + (6000 × 7 × 10/100)
= $6000 + (42000 × 10/100)
= $6000 + (420000/100)
= $6000 + $4200 = $10200
Thus, Amount (A) to be paid = $10200 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 10 years
= Simple interest for 1 year × 10
= $420 × 10 = $4200
Thus, Simple Interest (SI) = $4200
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $4200
= $10200
Thus, Amount to be paid = $10200 Answer
Similar Questions
(1) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(2) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?
(3) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 8 years.
(5) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6528 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?
(7) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(8) In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?
(9) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.
(10) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.