Question:
Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
Correct Answer
$6868
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 4%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 9
= $5050 ×4/100 × 9
= 5050 × 4 × 9/100
= 20200 × 9/100
= 181800/100
= $1818
Thus, Simple Interest = $1818
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 + $1818
= $6868
Thus, Amount to be paid = $6868 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) = 4%
And, Time (t) = 9 years
Thus, Amount (A)
= $5050 + ($5050 × 4% × 9)
= $5050 + ($5050 ×4/100 × 9)
= $5050 + (5050 × 4 × 9/100)
= $5050 + (20200 × 9/100)
= $5050 + (181800/100)
= $5050 + $1818 = $6868
Thus, Amount (A) to be paid = $6868 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5050, the simple interest in 1 year
= 4/100 × 5050
= 4 × 5050/100
= 20200/100 = $202
Thus, simple interest for 1 year = $202
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $202 × 9 = $1818
Thus, Simple Interest (SI) = $1818
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $1818
= $6868
Thus, Amount to be paid = $6868 Answer
Similar Questions
(1) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 7% simple interest?
(3) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 4 years.
(4) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(5) If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
(9) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(10) Paul had to pay $5405 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.