Question:
Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.
Correct Answer
$9546
Solution And Explanation
Solution
Given,
Principal (P) = $5550
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) = $5550 × 9% × 8
= $5550 ×9/100 × 8
= 5550 × 9 × 8/100
= 49950 × 8/100
= 399600/100
= $3996
Thus, Simple Interest = $3996
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 = $5550 + $3996
= $9546
Thus, Amount to be paid = $9546 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 = $5550
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5550 + ($5550 × 9% × 8)
= $5550 + ($5550 ×9/100 × 8)
= $5550 + (5550 × 9 × 8/100)
= $5550 + (49950 × 8/100)
= $5550 + (399600/100)
= $5550 + $3996 = $9546
Thus, Amount (A) to be paid = $9546 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 $5550, the simple interest in 1 year
= 9/100 × 5550
= 9 × 5550/100
= 49950/100 = $499.5
Thus, simple interest for 1 year = $499.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $499.5 × 8 = $3996
Thus, Simple Interest (SI) = $3996
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $3996
= $9546
Thus, Amount to be paid = $9546 Answer
Similar Questions
(1) Robert had to pay $3286 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 3% simple interest?
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.
(4) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
(5) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.
(6) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.
(8) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(9) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(10) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6120 to clear the loan, then find the time period of the loan.