Question:
Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.
Correct Answer
$7080
Solution And Explanation
Solution
Given,
Principal (P) = $5900
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) = $5900 × 2% × 10
= $5900 ×2/100 × 10
= 5900 × 2 × 10/100
= 11800 × 10/100
= 118000/100
= $1180
Thus, Simple Interest = $1180
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 = $5900 + $1180
= $7080
Thus, Amount to be paid = $7080 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 = $5900
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5900 + ($5900 × 2% × 10)
= $5900 + ($5900 ×2/100 × 10)
= $5900 + (5900 × 2 × 10/100)
= $5900 + (11800 × 10/100)
= $5900 + (118000/100)
= $5900 + $1180 = $7080
Thus, Amount (A) to be paid = $7080 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 $5900, the simple interest in 1 year
= 2/100 × 5900
= 2 × 5900/100
= 11800/100 = $118
Thus, simple interest for 1 year = $118
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $118 × 10 = $1180
Thus, Simple Interest (SI) = $1180
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $1180
= $7080
Thus, Amount to be paid = $7080 Answer
Similar Questions
(1) What amount does David have to pay after 5 years if he takes a loan of $3400 at 8% simple interest?
(2) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?
(3) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?
(4) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.
(5) How much loan did Mark borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7680 to clear it?
(6) How much loan did Betty borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7187.5 to clear it?
(7) If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) How much loan did Brian borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9000 to clear it?
(9) Steven had to pay $5014 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.