Question:
Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
Correct Answer
$10530
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 8%
Time (t) = 10 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% × 10
= $5850 ×8/100 × 10
= 5850 × 8 × 10/100
= 46800 × 10/100
= 468000/100
= $4680
Thus, Simple Interest = $4680
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 + $4680
= $10530
Thus, Amount to be paid = $10530 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) = 10 years
Thus, Amount (A)
= $5850 + ($5850 × 8% × 10)
= $5850 + ($5850 ×8/100 × 10)
= $5850 + (5850 × 8 × 10/100)
= $5850 + (46800 × 10/100)
= $5850 + (468000/100)
= $5850 + $4680 = $10530
Thus, Amount (A) to be paid = $10530 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 10 years
= Simple interest for 1 year × 10
= $468 × 10 = $4680
Thus, Simple Interest (SI) = $4680
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $4680
= $10530
Thus, Amount to be paid = $10530 Answer
Similar Questions
(1) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 2% simple interest?
(3) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 3 years.
(4) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(5) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(6) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8145 to clear the loan, then find the time period of the loan.
(7) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.
(9) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.
(10) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.