Question:
What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?
Correct Answer
$4550
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 6%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 5
= $3500 ×6/100 × 5
= 3500 × 6 × 5/100
= 21000 × 5/100
= 105000/100
= $1050
Thus, Simple Interest = $1050
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 + $1050
= $4550
Thus, Amount to be paid = $4550 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) = 6%
And, Time (t) = 5 years
Thus, Amount (A)
= $3500 + ($3500 × 6% × 5)
= $3500 + ($3500 ×6/100 × 5)
= $3500 + (3500 × 6 × 5/100)
= $3500 + (21000 × 5/100)
= $3500 + (105000/100)
= $3500 + $1050 = $4550
Thus, Amount (A) to be paid = $4550 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $3500, the simple interest in 1 year
= 6/100 × 3500
= 6 × 3500/100
= 21000/100 = $210
Thus, simple interest for 1 year = $210
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $210 × 5 = $1050
Thus, Simple Interest (SI) = $1050
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $1050
= $4550
Thus, Amount to be paid = $4550 Answer
Similar Questions
(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 7 years.
(2) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.
(4) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(5) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.
(7) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.
(8) How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?
(9) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(10) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.