Question:
What amount does John have to pay after 5 years if he takes a loan of $3200 at 7% simple interest?
Correct Answer
$4320
Solution And Explanation
Solution
Given,
Principal (P) = $3200
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) = $3200 × 7% × 5
= $3200 ×7/100 × 5
= 3200 × 7 × 5/100
= 22400 × 5/100
= 112000/100
= $1120
Thus, Simple Interest = $1120
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 = $3200 + $1120
= $4320
Thus, Amount to be paid = $4320 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 = $3200
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 5 years
Thus, Amount (A)
= $3200 + ($3200 × 7% × 5)
= $3200 + ($3200 ×7/100 × 5)
= $3200 + (3200 × 7 × 5/100)
= $3200 + (22400 × 5/100)
= $3200 + (112000/100)
= $3200 + $1120 = $4320
Thus, Amount (A) to be paid = $4320 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 $3200, the simple interest in 1 year
= 7/100 × 3200
= 7 × 3200/100
= 22400/100 = $224
Thus, simple interest for 1 year = $224
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $224 × 5 = $1120
Thus, Simple Interest (SI) = $1120
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3200 + $1120
= $4320
Thus, Amount to be paid = $4320 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(2) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?
(3) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(4) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 7 years.
(6) Anthony had to pay $4687 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(8) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?
(9) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(10) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.