Question:
What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 9% simple interest?
Correct Answer
$5698
Solution And Explanation
Solution
Given,
Principal (P) = $3700
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) = $3700 × 9% × 6
= $3700 ×9/100 × 6
= 3700 × 9 × 6/100
= 33300 × 6/100
= 199800/100
= $1998
Thus, Simple Interest = $1998
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 = $3700 + $1998
= $5698
Thus, Amount to be paid = $5698 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 = $3700
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 6 years
Thus, Amount (A)
= $3700 + ($3700 × 9% × 6)
= $3700 + ($3700 ×9/100 × 6)
= $3700 + (3700 × 9 × 6/100)
= $3700 + (33300 × 6/100)
= $3700 + (199800/100)
= $3700 + $1998 = $5698
Thus, Amount (A) to be paid = $5698 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 $3700, the simple interest in 1 year
= 9/100 × 3700
= 9 × 3700/100
= 33300/100 = $333
Thus, simple interest for 1 year = $333
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $333 × 6 = $1998
Thus, Simple Interest (SI) = $1998
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3700 + $1998
= $5698
Thus, Amount to be paid = $5698 Answer
Similar Questions
(1) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?
(2) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?
(4) What amount does James have to pay after 5 years if he takes a loan of $3000 at 4% simple interest?
(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(6) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?
(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
(8) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(9) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?