Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 7 years.
Correct Answer
$8165
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 6%
Time (t) = 7 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) = $5750 × 6% × 7
= $5750 ×6/100 × 7
= 5750 × 6 × 7/100
= 34500 × 7/100
= 241500/100
= $2415
Thus, Simple Interest = $2415
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 = $5750 + $2415
= $8165
Thus, Amount to be paid = $8165 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 = $5750
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 7 years
Thus, Amount (A)
= $5750 + ($5750 × 6% × 7)
= $5750 + ($5750 ×6/100 × 7)
= $5750 + (5750 × 6 × 7/100)
= $5750 + (34500 × 7/100)
= $5750 + (241500/100)
= $5750 + $2415 = $8165
Thus, Amount (A) to be paid = $8165 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 $5750, the simple interest in 1 year
= 6/100 × 5750
= 6 × 5750/100
= 34500/100 = $345
Thus, simple interest for 1 year = $345
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $345 × 7 = $2415
Thus, Simple Interest (SI) = $2415
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $2415
= $8165
Thus, Amount to be paid = $8165 Answer
Similar Questions
(1) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(2) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
(3) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(4) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.
(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 6% simple interest?
(6) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
(7) If Linda borrowed $3350 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(8) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
(9) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 8 years.