Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.
Correct Answer
$7897.5
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 5%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 7
= $5850 ×5/100 × 7
= 5850 × 5 × 7/100
= 29250 × 7/100
= 204750/100
= $2047.5
Thus, Simple Interest = $2047.5
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 + $2047.5
= $7897.5
Thus, Amount to be paid = $7897.5 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) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5850 + ($5850 × 5% × 7)
= $5850 + ($5850 ×5/100 × 7)
= $5850 + (5850 × 5 × 7/100)
= $5850 + (29250 × 7/100)
= $5850 + (204750/100)
= $5850 + $2047.5 = $7897.5
Thus, Amount (A) to be paid = $7897.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5850, the simple interest in 1 year
= 5/100 × 5850
= 5 × 5850/100
= 29250/100 = $292.5
Thus, simple interest for 1 year = $292.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $292.5 × 7 = $2047.5
Thus, Simple Interest (SI) = $2047.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $2047.5
= $7897.5
Thus, Amount to be paid = $7897.5 Answer
Similar Questions
(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 4 years.
(3) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 2% simple interest?
(4) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(5) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 4 years.
(7) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
(9) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.