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) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
(2) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.
(3) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?
(4) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(5) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?
(6) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?
(7) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 4 years.
(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?
(9) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(10) Robert had to pay $3472 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.