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) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?
(2) In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?
(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?
(5) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(6) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(7) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.
(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?
(9) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.