Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 7 years.
Correct Answer
$6885
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 5%
Time (t) = 7 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% × 7
= $5100 ×5/100 × 7
= 5100 × 5 × 7/100
= 25500 × 7/100
= 178500/100
= $1785
Thus, Simple Interest = $1785
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 + $1785
= $6885
Thus, Amount to be paid = $6885 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) = 7 years
Thus, Amount (A)
= $5100 + ($5100 × 5% × 7)
= $5100 + ($5100 ×5/100 × 7)
= $5100 + (5100 × 5 × 7/100)
= $5100 + (25500 × 7/100)
= $5100 + (178500/100)
= $5100 + $1785 = $6885
Thus, Amount (A) to be paid = $6885 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 7 years
= Simple interest for 1 year × 7
= $255 × 7 = $1785
Thus, Simple Interest (SI) = $1785
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $1785
= $6885
Thus, Amount to be paid = $6885 Answer
Similar Questions
(1) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(4) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
(5) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(6) If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.
(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(9) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?
(10) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?