Question:
Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
Correct Answer
$8850
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 5%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 10
= $5900 ×5/100 × 10
= 5900 × 5 × 10/100
= 29500 × 10/100
= 295000/100
= $2950
Thus, Simple Interest = $2950
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 + $2950
= $8850
Thus, Amount to be paid = $8850 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) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5900 + ($5900 × 5% × 10)
= $5900 + ($5900 ×5/100 × 10)
= $5900 + (5900 × 5 × 10/100)
= $5900 + (29500 × 10/100)
= $5900 + (295000/100)
= $5900 + $2950 = $8850
Thus, Amount (A) to be paid = $8850 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5900, the simple interest in 1 year
= 5/100 × 5900
= 5 × 5900/100
= 29500/100 = $295
Thus, simple interest for 1 year = $295
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $295 × 10 = $2950
Thus, Simple Interest (SI) = $2950
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $2950
= $8850
Thus, Amount to be paid = $8850 Answer
Similar Questions
(1) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?
(2) Mark had to pay $4664 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 8% simple interest?
(4) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?
(5) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
(6) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 7 years.
(8) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 3 years.
(10) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.