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) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?
(2) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 9% simple interest?
(3) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?
(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(5) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 7% simple interest?
(7) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(8) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 8 years.
(10) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.