Question:
What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 7% simple interest?
Correct Answer
$3990
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 7%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $3500 × 7% × 2
= $3500 ×7/100 × 2
= 3500 × 7 × 2/100
= 24500 × 2/100
= 49000/100
= $490
Thus, Simple Interest = $490
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 = $3500 + $490
= $3990
Thus, Amount to be paid = $3990 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 = $3500
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 2 years
Thus, Amount (A)
= $3500 + ($3500 × 7% × 2)
= $3500 + ($3500 ×7/100 × 2)
= $3500 + (3500 × 7 × 2/100)
= $3500 + (24500 × 2/100)
= $3500 + (49000/100)
= $3500 + $490 = $3990
Thus, Amount (A) to be paid = $3990 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3500, the simple interest in 1 year
= 7/100 × 3500
= 7 × 3500/100
= 24500/100 = $245
Thus, simple interest for 1 year = $245
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $245 × 2 = $490
Thus, Simple Interest (SI) = $490
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $490
= $3990
Thus, Amount to be paid = $3990 Answer
Similar Questions
(1) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
(2) If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?
(4) Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 2% simple interest?
(6) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 2% simple interest?
(7) 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.
(8) Margaret had to pay $4872 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
(10) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.