Question:
What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?
Correct Answer
$5365
Solution And Explanation
Solution
Given,
Principal (P) = $3700
Rate of Simple Interest (SI) = 9%
Time (t) = 5 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% × 5
= $3700 ×9/100 × 5
= 3700 × 9 × 5/100
= 33300 × 5/100
= 166500/100
= $1665
Thus, Simple Interest = $1665
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 + $1665
= $5365
Thus, Amount to be paid = $5365 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) = 5 years
Thus, Amount (A)
= $3700 + ($3700 × 9% × 5)
= $3700 + ($3700 ×9/100 × 5)
= $3700 + (3700 × 9 × 5/100)
= $3700 + (33300 × 5/100)
= $3700 + (166500/100)
= $3700 + $1665 = $5365
Thus, Amount (A) to be paid = $5365 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 5 years
= Simple interest for 1 year × 5
= $333 × 5 = $1665
Thus, Simple Interest (SI) = $1665
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3700 + $1665
= $5365
Thus, Amount to be paid = $5365 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.
(2) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(4) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.
(6) If Daniel paid $4428 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 3 years.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.
(10) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.