Question:
Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.
Correct Answer
$7410
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 3%
Time (t) = 10 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% × 10
= $5700 ×3/100 × 10
= 5700 × 3 × 10/100
= 17100 × 10/100
= 171000/100
= $1710
Thus, Simple Interest = $1710
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 + $1710
= $7410
Thus, Amount to be paid = $7410 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) = 10 years
Thus, Amount (A)
= $5700 + ($5700 × 3% × 10)
= $5700 + ($5700 ×3/100 × 10)
= $5700 + (5700 × 3 × 10/100)
= $5700 + (17100 × 10/100)
= $5700 + (171000/100)
= $5700 + $1710 = $7410
Thus, Amount (A) to be paid = $7410 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 10 years
= Simple interest for 1 year × 10
= $171 × 10 = $1710
Thus, Simple Interest (SI) = $1710
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $1710
= $7410
Thus, Amount to be paid = $7410 Answer
Similar Questions
(1) How much loan did Steven borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7590 to clear it?
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 8 years.
(3) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(4) If Susan paid $4380 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(6) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(8) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?
(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 4 years.
(10) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.