Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 8 years.
Correct Answer
$7956
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 8
= $5100 ×7/100 × 8
= 5100 × 7 × 8/100
= 35700 × 8/100
= 285600/100
= $2856
Thus, Simple Interest = $2856
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 + $2856
= $7956
Thus, Amount to be paid = $7956 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5100 + ($5100 × 7% × 8)
= $5100 + ($5100 ×7/100 × 8)
= $5100 + (5100 × 7 × 8/100)
= $5100 + (35700 × 8/100)
= $5100 + (285600/100)
= $5100 + $2856 = $7956
Thus, Amount (A) to be paid = $7956 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5100, the simple interest in 1 year
= 7/100 × 5100
= 7 × 5100/100
= 35700/100 = $357
Thus, simple interest for 1 year = $357
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $357 × 8 = $2856
Thus, Simple Interest (SI) = $2856
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $2856
= $7956
Thus, Amount to be paid = $7956 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
(2) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.
(5) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.
(6) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 3 years.
(8) If Anthony paid $4988 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 3 years.
(10) How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?