Question:
Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
Correct Answer
$7800
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 3%
Time (t) = 10 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% × 10
= $6000 ×3/100 × 10
= 6000 × 3 × 10/100
= 18000 × 10/100
= 180000/100
= $1800
Thus, Simple Interest = $1800
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 + $1800
= $7800
Thus, Amount to be paid = $7800 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) = 10 years
Thus, Amount (A)
= $6000 + ($6000 × 3% × 10)
= $6000 + ($6000 ×3/100 × 10)
= $6000 + (6000 × 3 × 10/100)
= $6000 + (18000 × 10/100)
= $6000 + (180000/100)
= $6000 + $1800 = $7800
Thus, Amount (A) to be paid = $7800 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 10 years
= Simple interest for 1 year × 10
= $180 × 10 = $1800
Thus, Simple Interest (SI) = $1800
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $1800
= $7800
Thus, Amount to be paid = $7800 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.
(2) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 8 years.
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 3 years.
(6) In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?
(7) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?
(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.
(10) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?