Question:
Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.
Correct Answer
$8774
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 8%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $5350 × 8% × 8
= $5350 ×8/100 × 8
= 5350 × 8 × 8/100
= 42800 × 8/100
= 342400/100
= $3424
Thus, Simple Interest = $3424
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 = $5350 + $3424
= $8774
Thus, Amount to be paid = $8774 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 = $5350
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5350 + ($5350 × 8% × 8)
= $5350 + ($5350 ×8/100 × 8)
= $5350 + (5350 × 8 × 8/100)
= $5350 + (42800 × 8/100)
= $5350 + (342400/100)
= $5350 + $3424 = $8774
Thus, Amount (A) to be paid = $8774 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5350, the simple interest in 1 year
= 8/100 × 5350
= 8 × 5350/100
= 42800/100 = $428
Thus, simple interest for 1 year = $428
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $428 × 8 = $3424
Thus, Simple Interest (SI) = $3424
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $3424
= $8774
Thus, Amount to be paid = $8774 Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
(2) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(3) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.
(4) How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.
(6) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?
(7) What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?
(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.
(9) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 5% simple interest?
(10) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.