Question:
Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
Correct Answer
$11210
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 10%
Time (t) = 9 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% × 9
= $5900 ×10/100 × 9
= 5900 × 10 × 9/100
= 59000 × 9/100
= 531000/100
= $5310
Thus, Simple Interest = $5310
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 + $5310
= $11210
Thus, Amount to be paid = $11210 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) = 9 years
Thus, Amount (A)
= $5900 + ($5900 × 10% × 9)
= $5900 + ($5900 ×10/100 × 9)
= $5900 + (5900 × 10 × 9/100)
= $5900 + (59000 × 9/100)
= $5900 + (531000/100)
= $5900 + $5310 = $11210
Thus, Amount (A) to be paid = $11210 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 9 years
= Simple interest for 1 year × 9
= $590 × 9 = $5310
Thus, Simple Interest (SI) = $5310
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $5310
= $11210
Thus, Amount to be paid = $11210 Answer
Similar Questions
(1) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?
(2) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.
(3) How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?
(4) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 3 years.
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 8 years.
(6) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 2% simple interest?
(7) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.
(8) How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?
(9) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 8 years.