Question:
What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 10% simple interest?
Correct Answer
$5550
Solution And Explanation
Solution
Given,
Principal (P) = $3700
Rate of Simple Interest (SI) = 10%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 5
= $3700 ×10/100 × 5
= 3700 × 10 × 5/100
= 37000 × 5/100
= 185000/100
= $1850
Thus, Simple Interest = $1850
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 + $1850
= $5550
Thus, Amount to be paid = $5550 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) = 10%
And, Time (t) = 5 years
Thus, Amount (A)
= $3700 + ($3700 × 10% × 5)
= $3700 + ($3700 ×10/100 × 5)
= $3700 + (3700 × 10 × 5/100)
= $3700 + (37000 × 5/100)
= $3700 + (185000/100)
= $3700 + $1850 = $5550
Thus, Amount (A) to be paid = $5550 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3700, the simple interest in 1 year
= 10/100 × 3700
= 10 × 3700/100
= 37000/100 = $370
Thus, simple interest for 1 year = $370
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $370 × 5 = $1850
Thus, Simple Interest (SI) = $1850
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3700 + $1850
= $5550
Thus, Amount to be paid = $5550 Answer
Similar Questions
(1) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.
(2) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.
(4) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(5) Ashley had to pay $5096 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.
(7) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
(8) How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?
(9) William had to pay $3815 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.