Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.
Correct Answer
$10620
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $5900 ×10/100 × 8
= 5900 × 10 × 8/100
= 59000 × 8/100
= 472000/100
= $4720
Thus, Simple Interest = $4720
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 + $4720
= $10620
Thus, Amount to be paid = $10620 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5900 + ($5900 × 10% × 8)
= $5900 + ($5900 ×10/100 × 8)
= $5900 + (5900 × 10 × 8/100)
= $5900 + (59000 × 8/100)
= $5900 + (472000/100)
= $5900 + $4720 = $10620
Thus, Amount (A) to be paid = $10620 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5900, the simple interest in 1 year
= 10/100 × 5900
= 10 × 5900/100
= 59000/100 = $590
Thus, simple interest for 1 year = $590
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $590 × 8 = $4720
Thus, Simple Interest (SI) = $4720
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $4720
= $10620
Thus, Amount to be paid = $10620 Answer
Similar Questions
(1) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(2) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 3 years.
(4) What amount will be due after 2 years if William borrowed a sum of $3250 at a 4% simple interest?
(5) 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?
(6) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?
(7) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?
(9) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 6% simple interest?
(10) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 3 years.