Question:
What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?
Correct Answer
$5850
Solution And Explanation
Solution
Given,
Principal (P) = $3900
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) = $3900 × 10% × 5
= $3900 ×10/100 × 5
= 3900 × 10 × 5/100
= 39000 × 5/100
= 195000/100
= $1950
Thus, Simple Interest = $1950
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 = $3900 + $1950
= $5850
Thus, Amount to be paid = $5850 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 = $3900
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 5 years
Thus, Amount (A)
= $3900 + ($3900 × 10% × 5)
= $3900 + ($3900 ×10/100 × 5)
= $3900 + (3900 × 10 × 5/100)
= $3900 + (39000 × 5/100)
= $3900 + (195000/100)
= $3900 + $1950 = $5850
Thus, Amount (A) to be paid = $5850 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 $3900, the simple interest in 1 year
= 10/100 × 3900
= 10 × 3900/100
= 39000/100 = $390
Thus, simple interest for 1 year = $390
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $390 × 5 = $1950
Thus, Simple Interest (SI) = $1950
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $1950
= $5850
Thus, Amount to be paid = $5850 Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(2) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?
(3) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 2% simple interest?
(4) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(5) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?
(6) Kenneth had to pay $5600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?
(8) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.