Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.
Correct Answer
$3751
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 7%
Time (t) = 3 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) = $3100 × 7% × 3
= $3100 ×7/100 × 3
= 3100 × 7 × 3/100
= 21700 × 3/100
= 65100/100
= $651
Thus, Simple Interest = $651
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 + $651
= $3751
Thus, Amount to be paid = $3751 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) = 7%
And, Time (t) = 3 years
Thus, Amount (A)
= $3100 + ($3100 × 7% × 3)
= $3100 + ($3100 ×7/100 × 3)
= $3100 + (3100 × 7 × 3/100)
= $3100 + (21700 × 3/100)
= $3100 + (65100/100)
= $3100 + $651 = $3751
Thus, Amount (A) to be paid = $3751 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 $3100, the simple interest in 1 year
= 7/100 × 3100
= 7 × 3100/100
= 21700/100 = $217
Thus, simple interest for 1 year = $217
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $217 × 3 = $651
Thus, Simple Interest (SI) = $651
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $651
= $3751
Thus, Amount to be paid = $3751 Answer
Similar Questions
(1) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 3% simple interest?
(2) In how much time a principal of $3100 will amount to $3472 at a simple interest of 4% per annum?
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(4) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.
(6) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 3 years.
(9) Richard had to pay $3924 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 3 years.