Question:
Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
Correct Answer
$9090
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 8%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 10
= $5050 ×8/100 × 10
= 5050 × 8 × 10/100
= 40400 × 10/100
= 404000/100
= $4040
Thus, Simple Interest = $4040
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 + $4040
= $9090
Thus, Amount to be paid = $9090 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) = 8%
And, Time (t) = 10 years
Thus, Amount (A)
= $5050 + ($5050 × 8% × 10)
= $5050 + ($5050 ×8/100 × 10)
= $5050 + (5050 × 8 × 10/100)
= $5050 + (40400 × 10/100)
= $5050 + (404000/100)
= $5050 + $4040 = $9090
Thus, Amount (A) to be paid = $9090 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5050, the simple interest in 1 year
= 8/100 × 5050
= 8 × 5050/100
= 40400/100 = $404
Thus, simple interest for 1 year = $404
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $404 × 10 = $4040
Thus, Simple Interest (SI) = $4040
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $4040
= $9090
Thus, Amount to be paid = $9090 Answer
Similar Questions
(1) How much loan did Kevin borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7810 to clear it?
(2) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 3 years.
(4) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9512 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.
(6) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.
(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?
(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.
(10) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 7% simple interest.