Question : Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
Correct Answer $8260
Solution & Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 4%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5900 × 4% × 10
= $5900 ×4/100 × 10
= 5900 × 4 × 10/100
= 23600 × 10/100
= 236000/100
= $2360
Thus, Simple Interest = $2360
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 = $5900 + $2360
= $8260
Thus, Amount to be paid = $8260 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 = $5900
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 10 years
Thus, Amount (A)
= $5900 + ($5900 × 4% × 10)
= $5900 + ($5900 ×4/100 × 10)
= $5900 + (5900 × 4 × 10/100)
= $5900 + (23600 × 10/100)
= $5900 + (236000/100)
= $5900 + $2360 = $8260
Thus, Amount (A) to be paid = $8260 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5900, the simple interest in 1 year
= 4/100 × 5900
= 4 × 5900/100
= 23600/100 = $236
Thus, simple interest for 1 year = $236
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $236 × 10 = $2360
Thus, Simple Interest (SI) = $2360
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $2360
= $8260
Thus, Amount to be paid = $8260 Answer
Similar Questions
(1) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?
(2) In how much time a principal of $3200 will amount to $3584 at a simple interest of 4% per annum?
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.
(5) In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?
(6) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 3 years.
(7) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?