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) How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?
(2) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.
(3) Joseph had to pay $4033 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.
(5) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.
(7) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(9) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.
(10) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?