Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 8 years.
Correct Answer
$7140
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $5100 × 5% × 8
= $5100 ×5/100 × 8
= 5100 × 5 × 8/100
= 25500 × 8/100
= 204000/100
= $2040
Thus, Simple Interest = $2040
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 = $5100 + $2040
= $7140
Thus, Amount to be paid = $7140 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 = $5100
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5100 + ($5100 × 5% × 8)
= $5100 + ($5100 ×5/100 × 8)
= $5100 + (5100 × 5 × 8/100)
= $5100 + (25500 × 8/100)
= $5100 + (204000/100)
= $5100 + $2040 = $7140
Thus, Amount (A) to be paid = $7140 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5100, the simple interest in 1 year
= 5/100 × 5100
= 5 × 5100/100
= 25500/100 = $255
Thus, simple interest for 1 year = $255
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $255 × 8 = $2040
Thus, Simple Interest (SI) = $2040
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $2040
= $7140
Thus, Amount to be paid = $7140 Answer
Similar Questions
(1) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(2) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 7 years.
(3) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.
(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.
(5) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 10% simple interest?
(6) If John borrowed $3200 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?
(8) What amount will be due after 2 years if James borrowed a sum of $3000 at a 10% simple interest?
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
(10) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?