Question:
Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.
Correct Answer
$9632
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (SI) = 9%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 8
= $5600 ×9/100 × 8
= 5600 × 9 × 8/100
= 50400 × 8/100
= 403200/100
= $4032
Thus, Simple Interest = $4032
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 + $4032
= $9632
Thus, Amount to be paid = $9632 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) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5600 + ($5600 × 9% × 8)
= $5600 + ($5600 ×9/100 × 8)
= $5600 + (5600 × 9 × 8/100)
= $5600 + (50400 × 8/100)
= $5600 + (403200/100)
= $5600 + $4032 = $9632
Thus, Amount (A) to be paid = $9632 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5600, the simple interest in 1 year
= 9/100 × 5600
= 9 × 5600/100
= 50400/100 = $504
Thus, simple interest for 1 year = $504
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $504 × 8 = $4032
Thus, Simple Interest (SI) = $4032
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $4032
= $9632
Thus, Amount to be paid = $9632 Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 3 years.
(2) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.
(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?
(4) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 9% simple interest?
(5) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.
(7) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(8) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(9) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.