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) Paul had to pay $5405 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?
(3) How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?
(4) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.
(5) Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.
(7) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.
(9) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 8% simple interest?
(10) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?