Question:
Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.
Correct Answer
$10226.5
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 9%
Time (t) = 9 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) = $5650 × 9% × 9
= $5650 ×9/100 × 9
= 5650 × 9 × 9/100
= 50850 × 9/100
= 457650/100
= $4576.5
Thus, Simple Interest = $4576.5
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 = $5650 + $4576.5
= $10226.5
Thus, Amount to be paid = $10226.5 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 = $5650
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5650 + ($5650 × 9% × 9)
= $5650 + ($5650 ×9/100 × 9)
= $5650 + (5650 × 9 × 9/100)
= $5650 + (50850 × 9/100)
= $5650 + (457650/100)
= $5650 + $4576.5 = $10226.5
Thus, Amount (A) to be paid = $10226.5 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 $5650, the simple interest in 1 year
= 9/100 × 5650
= 9 × 5650/100
= 50850/100 = $508.5
Thus, simple interest for 1 year = $508.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $508.5 × 9 = $4576.5
Thus, Simple Interest (SI) = $4576.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $4576.5
= $10226.5
Thus, Amount to be paid = $10226.5 Answer
Similar Questions
(1) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(2) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(3) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?
(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.
(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(7) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.
(8) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(9) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 10% simple interest?
(10) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8145 to clear the loan, then find the time period of the loan.