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) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 4 years.
(2) What amount does John have to pay after 6 years if he takes a loan of $3200 at 10% simple interest?
(3) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.
(4) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.
(6) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 7 years.
(8) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.
(9) Thomas had to pay $4028 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.