Question:
Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.
Correct Answer
$7540
Solution And Explanation
Solution
Given,
Principal (P) = $5800
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) = $5800 × 3% × 10
= $5800 ×3/100 × 10
= 5800 × 3 × 10/100
= 17400 × 10/100
= 174000/100
= $1740
Thus, Simple Interest = $1740
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 = $5800 + $1740
= $7540
Thus, Amount to be paid = $7540 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 = $5800
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5800 + ($5800 × 3% × 10)
= $5800 + ($5800 ×3/100 × 10)
= $5800 + (5800 × 3 × 10/100)
= $5800 + (17400 × 10/100)
= $5800 + (174000/100)
= $5800 + $1740 = $7540
Thus, Amount (A) to be paid = $7540 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 $5800, the simple interest in 1 year
= 3/100 × 5800
= 3 × 5800/100
= 17400/100 = $174
Thus, simple interest for 1 year = $174
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $174 × 10 = $1740
Thus, Simple Interest (SI) = $1740
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $1740
= $7540
Thus, Amount to be paid = $7540 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(2) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
(3) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(4) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 7% simple interest?
(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 7 years.
(7) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?
(9) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?
(10) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.