Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
Correct Answer
$7130
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5750 ×3/100 × 8
= 5750 × 3 × 8/100
= 17250 × 8/100
= 138000/100
= $1380
Thus, Simple Interest = $1380
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 + $1380
= $7130
Thus, Amount to be paid = $7130 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5750 + ($5750 × 3% × 8)
= $5750 + ($5750 ×3/100 × 8)
= $5750 + (5750 × 3 × 8/100)
= $5750 + (17250 × 8/100)
= $5750 + (138000/100)
= $5750 + $1380 = $7130
Thus, Amount (A) to be paid = $7130 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5750, the simple interest in 1 year
= 3/100 × 5750
= 3 × 5750/100
= 17250/100 = $172.5
Thus, simple interest for 1 year = $172.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $172.5 × 8 = $1380
Thus, Simple Interest (SI) = $1380
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $1380
= $7130
Thus, Amount to be paid = $7130 Answer
Similar Questions
(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?
(2) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 3 years.
(5) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 3 years.
(6) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(7) How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?
(8) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 3 years.
(9) What amount will be due after 2 years if William borrowed a sum of $3250 at a 6% simple interest?
(10) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 8% simple interest?