Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.
Correct Answer
$7068
Solution And Explanation
Solution
Given,
Principal (P) = $5700
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) = $5700 × 3% × 8
= $5700 ×3/100 × 8
= 5700 × 3 × 8/100
= 17100 × 8/100
= 136800/100
= $1368
Thus, Simple Interest = $1368
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 = $5700 + $1368
= $7068
Thus, Amount to be paid = $7068 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 = $5700
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5700 + ($5700 × 3% × 8)
= $5700 + ($5700 ×3/100 × 8)
= $5700 + (5700 × 3 × 8/100)
= $5700 + (17100 × 8/100)
= $5700 + (136800/100)
= $5700 + $1368 = $7068
Thus, Amount (A) to be paid = $7068 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 $5700, the simple interest in 1 year
= 3/100 × 5700
= 3 × 5700/100
= 17100/100 = $171
Thus, simple interest for 1 year = $171
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $171 × 8 = $1368
Thus, Simple Interest (SI) = $1368
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $1368
= $7068
Thus, Amount to be paid = $7068 Answer
Similar Questions
(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.
(2) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 8 years.
(5) If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 4 years.
(8) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 3 years.