Question:
Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
Correct Answer
$9360
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 6%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 10
= $5850 ×6/100 × 10
= 5850 × 6 × 10/100
= 35100 × 10/100
= 351000/100
= $3510
Thus, Simple Interest = $3510
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 + $3510
= $9360
Thus, Amount to be paid = $9360 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) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5850 + ($5850 × 6% × 10)
= $5850 + ($5850 ×6/100 × 10)
= $5850 + (5850 × 6 × 10/100)
= $5850 + (35100 × 10/100)
= $5850 + (351000/100)
= $5850 + $3510 = $9360
Thus, Amount (A) to be paid = $9360 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5850, the simple interest in 1 year
= 6/100 × 5850
= 6 × 5850/100
= 35100/100 = $351
Thus, simple interest for 1 year = $351
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $351 × 10 = $3510
Thus, Simple Interest (SI) = $3510
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $3510
= $9360
Thus, Amount to be paid = $9360 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.
(3) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?
(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?
(5) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.
(6) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.
(8) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 8 years.
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 7 years.
(10) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.