Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 8 years.
Correct Answer
$8970
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 8
= $5750 ×7/100 × 8
= 5750 × 7 × 8/100
= 40250 × 8/100
= 322000/100
= $3220
Thus, Simple Interest = $3220
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 + $3220
= $8970
Thus, Amount to be paid = $8970 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5750 + ($5750 × 7% × 8)
= $5750 + ($5750 ×7/100 × 8)
= $5750 + (5750 × 7 × 8/100)
= $5750 + (40250 × 8/100)
= $5750 + (322000/100)
= $5750 + $3220 = $8970
Thus, Amount (A) to be paid = $8970 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5750, the simple interest in 1 year
= 7/100 × 5750
= 7 × 5750/100
= 40250/100 = $402.5
Thus, simple interest for 1 year = $402.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $402.5 × 8 = $3220
Thus, Simple Interest (SI) = $3220
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $3220
= $8970
Thus, Amount to be paid = $8970 Answer
Similar Questions
(1) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(2) What amount does James have to pay after 5 years if he takes a loan of $3000 at 8% simple interest?
(3) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(4) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 8% simple interest?
(5) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 7 years.
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.
(7) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?
(9) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?
(10) If Susan borrowed $3650 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.