Question:
What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?
Correct Answer
$4070
Solution And Explanation
Solution
Given,
Principal (P) = $3700
Rate of Simple Interest (SI) = 5%
Time (t) = 2 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) = $3700 × 5% × 2
= $3700 ×5/100 × 2
= 3700 × 5 × 2/100
= 18500 × 2/100
= 37000/100
= $370
Thus, Simple Interest = $370
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 = $3700 + $370
= $4070
Thus, Amount to be paid = $4070 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 = $3700
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 2 years
Thus, Amount (A)
= $3700 + ($3700 × 5% × 2)
= $3700 + ($3700 ×5/100 × 2)
= $3700 + (3700 × 5 × 2/100)
= $3700 + (18500 × 2/100)
= $3700 + (37000/100)
= $3700 + $370 = $4070
Thus, Amount (A) to be paid = $4070 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 $3700, the simple interest in 1 year
= 5/100 × 3700
= 5 × 3700/100
= 18500/100 = $185
Thus, simple interest for 1 year = $185
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $185 × 2 = $370
Thus, Simple Interest (SI) = $370
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3700 + $370
= $4070
Thus, Amount to be paid = $4070 Answer
Similar Questions
(1) What amount does James have to pay after 5 years if he takes a loan of $3000 at 3% simple interest?
(2) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(3) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.
(5) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(6) 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.
(7) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.
(8) If John paid $3840 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 James borrowed a sum of $5000 at a rate of 9% simple interest.
(10) How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?