Question:
Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
Correct Answer
$8701
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 6%
Time (t) = 9 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) = $5650 × 6% × 9
= $5650 ×6/100 × 9
= 5650 × 6 × 9/100
= 33900 × 9/100
= 305100/100
= $3051
Thus, Simple Interest = $3051
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 + $3051
= $8701
Thus, Amount to be paid = $8701 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) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5650 + ($5650 × 6% × 9)
= $5650 + ($5650 ×6/100 × 9)
= $5650 + (5650 × 6 × 9/100)
= $5650 + (33900 × 9/100)
= $5650 + (305100/100)
= $5650 + $3051 = $8701
Thus, Amount (A) to be paid = $8701 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 $5650, the simple interest in 1 year
= 6/100 × 5650
= 6 × 5650/100
= 33900/100 = $339
Thus, simple interest for 1 year = $339
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $339 × 9 = $3051
Thus, Simple Interest (SI) = $3051
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $3051
= $8701
Thus, Amount to be paid = $8701 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(2) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.
(4) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(5) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3200 will amount to $3520 at a simple interest of 5% per annum?
(7) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 3 years.
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 8% simple interest?
(9) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(10) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.