Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.
Correct Answer
$6262
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5050 ×3/100 × 8
= 5050 × 3 × 8/100
= 15150 × 8/100
= 121200/100
= $1212
Thus, Simple Interest = $1212
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 + $1212
= $6262
Thus, Amount to be paid = $6262 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5050 + ($5050 × 3% × 8)
= $5050 + ($5050 ×3/100 × 8)
= $5050 + (5050 × 3 × 8/100)
= $5050 + (15150 × 8/100)
= $5050 + (121200/100)
= $5050 + $1212 = $6262
Thus, Amount (A) to be paid = $6262 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5050, the simple interest in 1 year
= 3/100 × 5050
= 3 × 5050/100
= 15150/100 = $151.5
Thus, simple interest for 1 year = $151.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $151.5 × 8 = $1212
Thus, Simple Interest (SI) = $1212
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $1212
= $6262
Thus, Amount to be paid = $6262 Answer
Similar Questions
(1) Donald had to pay $4770 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?
(4) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.
(5) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(6) If Susan borrowed $3650 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 2% simple interest?
(8) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8050 to clear it?
(9) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 2% simple interest?