Question:
Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
Correct Answer
$10640
Solution And Explanation
Solution
Given,
Principal (P) = $5600
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) = $5600 × 10% × 9
= $5600 ×10/100 × 9
= 5600 × 10 × 9/100
= 56000 × 9/100
= 504000/100
= $5040
Thus, Simple Interest = $5040
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 = $5600 + $5040
= $10640
Thus, Amount to be paid = $10640 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 = $5600
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5600 + ($5600 × 10% × 9)
= $5600 + ($5600 ×10/100 × 9)
= $5600 + (5600 × 10 × 9/100)
= $5600 + (56000 × 9/100)
= $5600 + (504000/100)
= $5600 + $5040 = $10640
Thus, Amount (A) to be paid = $10640 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 $5600, the simple interest in 1 year
= 10/100 × 5600
= 10 × 5600/100
= 56000/100 = $560
Thus, simple interest for 1 year = $560
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $560 × 9 = $5040
Thus, Simple Interest (SI) = $5040
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $5040
= $10640
Thus, Amount to be paid = $10640 Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(2) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(3) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 9% simple interest?
(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 3 years.
(5) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 4% simple interest?
(6) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?
(7) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 4 years.
(8) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 4 years.
(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.