Question:
Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.
Correct Answer
$6840
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 2%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $5700 × 2% × 10
= $5700 ×2/100 × 10
= 5700 × 2 × 10/100
= 11400 × 10/100
= 114000/100
= $1140
Thus, Simple Interest = $1140
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 = $5700 + $1140
= $6840
Thus, Amount to be paid = $6840 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 = $5700
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5700 + ($5700 × 2% × 10)
= $5700 + ($5700 ×2/100 × 10)
= $5700 + (5700 × 2 × 10/100)
= $5700 + (11400 × 10/100)
= $5700 + (114000/100)
= $5700 + $1140 = $6840
Thus, Amount (A) to be paid = $6840 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5700, the simple interest in 1 year
= 2/100 × 5700
= 2 × 5700/100
= 11400/100 = $114
Thus, simple interest for 1 year = $114
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $114 × 10 = $1140
Thus, Simple Interest (SI) = $1140
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $1140
= $6840
Thus, Amount to be paid = $6840 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 4 years.
(3) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.
(5) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(6) Linda had to pay $3651.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) In how much time a principal of $3150 will amount to $3528 at a simple interest of 3% per annum?
(9) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(10) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.