Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.
Correct Answer
$7171
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 6%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 7
= $5050 ×6/100 × 7
= 5050 × 6 × 7/100
= 30300 × 7/100
= 212100/100
= $2121
Thus, Simple Interest = $2121
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 + $2121
= $7171
Thus, Amount to be paid = $7171 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) = 6%
And, Time (t) = 7 years
Thus, Amount (A)
= $5050 + ($5050 × 6% × 7)
= $5050 + ($5050 ×6/100 × 7)
= $5050 + (5050 × 6 × 7/100)
= $5050 + (30300 × 7/100)
= $5050 + (212100/100)
= $5050 + $2121 = $7171
Thus, Amount (A) to be paid = $7171 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5050, the simple interest in 1 year
= 6/100 × 5050
= 6 × 5050/100
= 30300/100 = $303
Thus, simple interest for 1 year = $303
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $303 × 7 = $2121
Thus, Simple Interest (SI) = $2121
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $2121
= $7171
Thus, Amount to be paid = $7171 Answer
Similar Questions
(1) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 3 years.
(4) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 8% simple interest?
(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 4 years.
(6) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?
(8) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?
(9) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.
(10) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.