Question:
What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?
Correct Answer
$5544
Solution And Explanation
Solution
Given,
Principal (P) = $3600
Rate of Simple Interest (SI) = 9%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 6
= $3600 ×9/100 × 6
= 3600 × 9 × 6/100
= 32400 × 6/100
= 194400/100
= $1944
Thus, Simple Interest = $1944
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 + $1944
= $5544
Thus, Amount to be paid = $5544 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) = 9%
And, Time (t) = 6 years
Thus, Amount (A)
= $3600 + ($3600 × 9% × 6)
= $3600 + ($3600 ×9/100 × 6)
= $3600 + (3600 × 9 × 6/100)
= $3600 + (32400 × 6/100)
= $3600 + (194400/100)
= $3600 + $1944 = $5544
Thus, Amount (A) to be paid = $5544 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3600, the simple interest in 1 year
= 9/100 × 3600
= 9 × 3600/100
= 32400/100 = $324
Thus, simple interest for 1 year = $324
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $324 × 6 = $1944
Thus, Simple Interest (SI) = $1944
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3600 + $1944
= $5544
Thus, Amount to be paid = $5544 Answer
Similar Questions
(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.
(2) How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?
(3) Donald had to pay $4770 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) If Mary borrowed $3050 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(6) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.
(7) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.
(8) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(9) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(10) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.