Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 8 years.
Correct Answer
$8686
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 9%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 8
= $5050 ×9/100 × 8
= 5050 × 9 × 8/100
= 45450 × 8/100
= 363600/100
= $3636
Thus, Simple Interest = $3636
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 + $3636
= $8686
Thus, Amount to be paid = $8686 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) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5050 + ($5050 × 9% × 8)
= $5050 + ($5050 ×9/100 × 8)
= $5050 + (5050 × 9 × 8/100)
= $5050 + (45450 × 8/100)
= $5050 + (363600/100)
= $5050 + $3636 = $8686
Thus, Amount (A) to be paid = $8686 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5050, the simple interest in 1 year
= 9/100 × 5050
= 9 × 5050/100
= 45450/100 = $454.5
Thus, simple interest for 1 year = $454.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $454.5 × 8 = $3636
Thus, Simple Interest (SI) = $3636
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $3636
= $8686
Thus, Amount to be paid = $8686 Answer
Similar Questions
(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 3% simple interest?
(2) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?
(4) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(5) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 9% simple interest?
(6) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(7) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 10% simple interest?
(8) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.
(9) If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.