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) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(2) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(3) How much loan did Robert borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5865 to clear it?
(4) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?
(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.
(6) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 10% simple interest?
(7) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(8) If Andrew paid $5760 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(10) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.