Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 8 years.
Correct Answer
$9090
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $5050 ×10/100 × 8
= 5050 × 10 × 8/100
= 50500 × 8/100
= 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5050 + ($5050 × 10% × 8)
= $5050 + ($5050 ×10/100 × 8)
= $5050 + (5050 × 10 × 8/100)
= $5050 + (50500 × 8/100)
= $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 = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5050, the simple interest in 1 year
= 10/100 × 5050
= 10 × 5050/100
= 50500/100 = $505
Thus, simple interest for 1 year = $505
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $505 × 8 = $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) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(2) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?
(3) How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.
(5) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.
(8) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $12200 to clear the loan, then find the time period of the loan.
(9) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?
(10) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?