Question:
What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?
Correct Answer
$4030
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 6%
Time (t) = 5 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) = $3100 × 6% × 5
= $3100 ×6/100 × 5
= 3100 × 6 × 5/100
= 18600 × 5/100
= 93000/100
= $930
Thus, Simple Interest = $930
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 = $3100 + $930
= $4030
Thus, Amount to be paid = $4030 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 = $3100
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 5 years
Thus, Amount (A)
= $3100 + ($3100 × 6% × 5)
= $3100 + ($3100 ×6/100 × 5)
= $3100 + (3100 × 6 × 5/100)
= $3100 + (18600 × 5/100)
= $3100 + (93000/100)
= $3100 + $930 = $4030
Thus, Amount (A) to be paid = $4030 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 $3100, the simple interest in 1 year
= 6/100 × 3100
= 6 × 3100/100
= 18600/100 = $186
Thus, simple interest for 1 year = $186
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $186 × 5 = $930
Thus, Simple Interest (SI) = $930
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $930
= $4030
Thus, Amount to be paid = $4030 Answer
Similar Questions
(1) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?
(2) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.
(3) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 3 years.
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 3 years.
(6) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3100 will amount to $3348 at a simple interest of 2% per annum?
(8) How much loan did Melissa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8085 to clear it?
(9) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 2% simple interest?
(10) If Karen paid $4266 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.