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) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.
(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
(5) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?
(7) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 3 years.
(8) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9536 to clear the loan, then find the time period of the loan.
(9) Charles had to pay $4368 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?