Question:
Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
Correct Answer
$8585
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 7%
Time (t) = 10 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) = $5050 × 7% × 10
= $5050 ×7/100 × 10
= 5050 × 7 × 10/100
= 35350 × 10/100
= 353500/100
= $3535
Thus, Simple Interest = $3535
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 = $5050 + $3535
= $8585
Thus, Amount to be paid = $8585 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 = $5050
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5050 + ($5050 × 7% × 10)
= $5050 + ($5050 ×7/100 × 10)
= $5050 + (5050 × 7 × 10/100)
= $5050 + (35350 × 10/100)
= $5050 + (353500/100)
= $5050 + $3535 = $8585
Thus, Amount (A) to be paid = $8585 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 $5050, the simple interest in 1 year
= 7/100 × 5050
= 7 × 5050/100
= 35350/100 = $353.5
Thus, simple interest for 1 year = $353.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $353.5 × 10 = $3535
Thus, Simple Interest (SI) = $3535
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $3535
= $8585
Thus, Amount to be paid = $8585 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 3 years.
(2) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.
(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(5) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(6) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9180 to clear it?
(7) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?
(8) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?
(10) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.