Question:
What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?
Correct Answer
$5112
Solution And Explanation
Solution
Given,
Principal (P) = $3600
Rate of Simple Interest (SI) = 7%
Time (t) = 6 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) = $3600 × 7% × 6
= $3600 ×7/100 × 6
= 3600 × 7 × 6/100
= 25200 × 6/100
= 151200/100
= $1512
Thus, Simple Interest = $1512
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 = $3600 + $1512
= $5112
Thus, Amount to be paid = $5112 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 = $3600
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 6 years
Thus, Amount (A)
= $3600 + ($3600 × 7% × 6)
= $3600 + ($3600 ×7/100 × 6)
= $3600 + (3600 × 7 × 6/100)
= $3600 + (25200 × 6/100)
= $3600 + (151200/100)
= $3600 + $1512 = $5112
Thus, Amount (A) to be paid = $5112 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 $3600, the simple interest in 1 year
= 7/100 × 3600
= 7 × 3600/100
= 25200/100 = $252
Thus, simple interest for 1 year = $252
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $252 × 6 = $1512
Thus, Simple Interest (SI) = $1512
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3600 + $1512
= $5112
Thus, Amount to be paid = $5112 Answer
Similar Questions
(1) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 7 years.
(2) How much loan did Lisa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6655 to clear it?
(3) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 8 years.
(5) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.
(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(9) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(10) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.