Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.
Correct Answer
$9594
Solution And Explanation
Solution
Given,
Principal (P) = $5850
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) = $5850 × 8% × 8
= $5850 ×8/100 × 8
= 5850 × 8 × 8/100
= 46800 × 8/100
= 374400/100
= $3744
Thus, Simple Interest = $3744
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 = $5850 + $3744
= $9594
Thus, Amount to be paid = $9594 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 = $5850
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5850 + ($5850 × 8% × 8)
= $5850 + ($5850 ×8/100 × 8)
= $5850 + (5850 × 8 × 8/100)
= $5850 + (46800 × 8/100)
= $5850 + (374400/100)
= $5850 + $3744 = $9594
Thus, Amount (A) to be paid = $9594 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 $5850, the simple interest in 1 year
= 8/100 × 5850
= 8 × 5850/100
= 46800/100 = $468
Thus, simple interest for 1 year = $468
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $468 × 8 = $3744
Thus, Simple Interest (SI) = $3744
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $3744
= $9594
Thus, Amount to be paid = $9594 Answer
Similar Questions
(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?
(2) If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 4 years.
(5) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(6) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?
(7) How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?
(8) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(9) What amount does John have to pay after 5 years if he takes a loan of $3200 at 6% simple interest?
(10) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?