Question:
Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
Correct Answer
$5959
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 2%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 9
= $5050 ×2/100 × 9
= 5050 × 2 × 9/100
= 10100 × 9/100
= 90900/100
= $909
Thus, Simple Interest = $909
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 + $909
= $5959
Thus, Amount to be paid = $5959 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) = 2%
And, Time (t) = 9 years
Thus, Amount (A)
= $5050 + ($5050 × 2% × 9)
= $5050 + ($5050 ×2/100 × 9)
= $5050 + (5050 × 2 × 9/100)
= $5050 + (10100 × 9/100)
= $5050 + (90900/100)
= $5050 + $909 = $5959
Thus, Amount (A) to be paid = $5959 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5050, the simple interest in 1 year
= 2/100 × 5050
= 2 × 5050/100
= 10100/100 = $101
Thus, simple interest for 1 year = $101
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $101 × 9 = $909
Thus, Simple Interest (SI) = $909
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $909
= $5959
Thus, Amount to be paid = $5959 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 8 years.
(3) If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9800 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.
(6) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.
(7) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 2% simple interest?
(8) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?
(9) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 3 years.