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) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 7 years.
(2) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?
(3) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9384 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 7% simple interest?
(5) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 2% simple interest?
(6) If Kimberly paid $5580 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Christopher had to pay $4480 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Mary had to pay $3507.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?