Question:
Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.
Correct Answer
$9990
Solution And Explanation
Solution
Given,
Principal (P) = $5550
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) = $5550 × 10% × 8
= $5550 ×10/100 × 8
= 5550 × 10 × 8/100
= 55500 × 8/100
= 444000/100
= $4440
Thus, Simple Interest = $4440
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 + $4440
= $9990
Thus, Amount to be paid = $9990 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5550 + ($5550 × 10% × 8)
= $5550 + ($5550 ×10/100 × 8)
= $5550 + (5550 × 10 × 8/100)
= $5550 + (55500 × 8/100)
= $5550 + (444000/100)
= $5550 + $4440 = $9990
Thus, Amount (A) to be paid = $9990 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 $5550, the simple interest in 1 year
= 10/100 × 5550
= 10 × 5550/100
= 55500/100 = $555
Thus, simple interest for 1 year = $555
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $555 × 8 = $4440
Thus, Simple Interest (SI) = $4440
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $4440
= $9990
Thus, Amount to be paid = $9990 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.
(3) 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?
(4) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(5) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.
(6) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?
(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 3 years.
(9) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11403 to clear the loan, then find the time period of the loan.
(10) If Karen borrowed $3950 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.