Question:
Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
Correct Answer
$8231.5
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 7%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 9
= $5050 ×7/100 × 9
= 5050 × 7 × 9/100
= 35350 × 9/100
= 318150/100
= $3181.5
Thus, Simple Interest = $3181.5
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 + $3181.5
= $8231.5
Thus, Amount to be paid = $8231.5 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) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5050 + ($5050 × 7% × 9)
= $5050 + ($5050 ×7/100 × 9)
= $5050 + (5050 × 7 × 9/100)
= $5050 + (35350 × 9/100)
= $5050 + (318150/100)
= $5050 + $3181.5 = $8231.5
Thus, Amount (A) to be paid = $8231.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5050, the simple interest in 1 year
= 7/100 × 5050
= 7 × 5050/100
= 35350/100 = $353.5
Thus, simple interest for 1 year = $353.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $353.5 × 9 = $3181.5
Thus, Simple Interest (SI) = $3181.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $3181.5
= $8231.5
Thus, Amount to be paid = $8231.5 Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.
(2) If James borrowed $3000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(4) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6664 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 3 years.
(6) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?
(7) If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 7 years.
(10) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.