Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.
Correct Answer
$7695
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 5%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 7
= $5700 ×5/100 × 7
= 5700 × 5 × 7/100
= 28500 × 7/100
= 199500/100
= $1995
Thus, Simple Interest = $1995
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 + $1995
= $7695
Thus, Amount to be paid = $7695 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) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5700 + ($5700 × 5% × 7)
= $5700 + ($5700 ×5/100 × 7)
= $5700 + (5700 × 5 × 7/100)
= $5700 + (28500 × 7/100)
= $5700 + (199500/100)
= $5700 + $1995 = $7695
Thus, Amount (A) to be paid = $7695 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5700, the simple interest in 1 year
= 5/100 × 5700
= 5 × 5700/100
= 28500/100 = $285
Thus, simple interest for 1 year = $285
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $285 × 7 = $1995
Thus, Simple Interest (SI) = $1995
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $1995
= $7695
Thus, Amount to be paid = $7695 Answer
Similar Questions
(1) Ashley had to pay $5232.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 4 years.
(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 3 years.
(4) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(5) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?
(7) How much loan did Mark borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7680 to clear it?
(8) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(9) What amount does William have to pay after 6 years if he takes a loan of $3500 at 6% simple interest?
(10) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?