Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 8 years.
Correct Answer
$8364
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 8%
Time (t) = 8 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) = $5100 × 8% × 8
= $5100 ×8/100 × 8
= 5100 × 8 × 8/100
= 40800 × 8/100
= 326400/100
= $3264
Thus, Simple Interest = $3264
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 + $3264
= $8364
Thus, Amount to be paid = $8364 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) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5100 + ($5100 × 8% × 8)
= $5100 + ($5100 ×8/100 × 8)
= $5100 + (5100 × 8 × 8/100)
= $5100 + (40800 × 8/100)
= $5100 + (326400/100)
= $5100 + $3264 = $8364
Thus, Amount (A) to be paid = $8364 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 $5100, the simple interest in 1 year
= 8/100 × 5100
= 8 × 5100/100
= 40800/100 = $408
Thus, simple interest for 1 year = $408
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $408 × 8 = $3264
Thus, Simple Interest (SI) = $3264
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $3264
= $8364
Thus, Amount to be paid = $8364 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.
(3) If Richard borrowed $3600 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) How much loan did Richard borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7000 to clear it?
(5) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(6) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 9% simple interest?
(7) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.
(8) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?
(9) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(10) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 10% simple interest?