Question:
Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.
Correct Answer
$8160
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 6%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 10
= $5100 ×6/100 × 10
= 5100 × 6 × 10/100
= 30600 × 10/100
= 306000/100
= $3060
Thus, Simple Interest = $3060
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 + $3060
= $8160
Thus, Amount to be paid = $8160 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) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5100 + ($5100 × 6% × 10)
= $5100 + ($5100 ×6/100 × 10)
= $5100 + (5100 × 6 × 10/100)
= $5100 + (30600 × 10/100)
= $5100 + (306000/100)
= $5100 + $3060 = $8160
Thus, Amount (A) to be paid = $8160 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5100, the simple interest in 1 year
= 6/100 × 5100
= 6 × 5100/100
= 30600/100 = $306
Thus, simple interest for 1 year = $306
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $306 × 10 = $3060
Thus, Simple Interest (SI) = $3060
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $3060
= $8160
Thus, Amount to be paid = $8160 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(2) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 3% simple interest?
(3) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(4) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?
(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 9% simple interest?
(6) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(7) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?
(9) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.
(10) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.