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) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.
(2) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6540 to clear it?
(3) Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) How much loan did Richard borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7000 to clear it?
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.
(6) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.
(8) If Jennifer paid $3510 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 7% simple interest?
(10) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6258 to clear the loan, then find the time period of the loan.