Question:
What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?
Correct Answer
$5460
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 8%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 5
= $3900 ×8/100 × 5
= 3900 × 8 × 5/100
= 31200 × 5/100
= 156000/100
= $1560
Thus, Simple Interest = $1560
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 + $1560
= $5460
Thus, Amount to be paid = $5460 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) = 8%
And, Time (t) = 5 years
Thus, Amount (A)
= $3900 + ($3900 × 8% × 5)
= $3900 + ($3900 ×8/100 × 5)
= $3900 + (3900 × 8 × 5/100)
= $3900 + (31200 × 5/100)
= $3900 + (156000/100)
= $3900 + $1560 = $5460
Thus, Amount (A) to be paid = $5460 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $3900, the simple interest in 1 year
= 8/100 × 3900
= 8 × 3900/100
= 31200/100 = $312
Thus, simple interest for 1 year = $312
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $312 × 5 = $1560
Thus, Simple Interest (SI) = $1560
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $1560
= $5460
Thus, Amount to be paid = $5460 Answer
Similar Questions
(1) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 4 years.
(2) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 2% simple interest.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.
(4) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.
(5) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.
(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.
(8) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?
(9) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 7 years.
(10) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?