Question:
What amount does David have to pay after 5 years if he takes a loan of $3400 at 7% simple interest?
Correct Answer
$4590
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 7%
Time (t) = 5 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) = $3400 × 7% × 5
= $3400 ×7/100 × 5
= 3400 × 7 × 5/100
= 23800 × 5/100
= 119000/100
= $1190
Thus, Simple Interest = $1190
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 = $3400 + $1190
= $4590
Thus, Amount to be paid = $4590 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 = $3400
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 5 years
Thus, Amount (A)
= $3400 + ($3400 × 7% × 5)
= $3400 + ($3400 ×7/100 × 5)
= $3400 + (3400 × 7 × 5/100)
= $3400 + (23800 × 5/100)
= $3400 + (119000/100)
= $3400 + $1190 = $4590
Thus, Amount (A) to be paid = $4590 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 $3400, the simple interest in 1 year
= 7/100 × 3400
= 7 × 3400/100
= 23800/100 = $238
Thus, simple interest for 1 year = $238
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $238 × 5 = $1190
Thus, Simple Interest (SI) = $1190
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $1190
= $4590
Thus, Amount to be paid = $4590 Answer
Similar Questions
(1) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?
(2) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?
(4) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.
(5) If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.
(7) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
(8) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.
(10) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.