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) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?
(2) Christopher had to pay $4360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(4) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?
(6) If Mary paid $3660 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 4 years.
(8) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?
(9) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(10) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.