Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.
Correct Answer
$9126
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 8%
Time (t) = 7 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% × 7
= $5850 ×8/100 × 7
= 5850 × 8 × 7/100
= 46800 × 7/100
= 327600/100
= $3276
Thus, Simple Interest = $3276
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 + $3276
= $9126
Thus, Amount to be paid = $9126 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) = 7 years
Thus, Amount (A)
= $5850 + ($5850 × 8% × 7)
= $5850 + ($5850 ×8/100 × 7)
= $5850 + (5850 × 8 × 7/100)
= $5850 + (46800 × 7/100)
= $5850 + (327600/100)
= $5850 + $3276 = $9126
Thus, Amount (A) to be paid = $9126 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 7 years
= Simple interest for 1 year × 7
= $468 × 7 = $3276
Thus, Simple Interest (SI) = $3276
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $3276
= $9126
Thus, Amount to be paid = $9126 Answer
Similar Questions
(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 8 years.
(2) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.
(4) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(5) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(6) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.
(7) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 3% simple interest?
(9) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 8 years.