Question:
Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
Correct Answer
$9698.5
Solution And Explanation
Solution
Given,
Principal (P) = $5950
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) = $5950 × 7% × 9
= $5950 ×7/100 × 9
= 5950 × 7 × 9/100
= 41650 × 9/100
= 374850/100
= $3748.5
Thus, Simple Interest = $3748.5
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 = $5950 + $3748.5
= $9698.5
Thus, Amount to be paid = $9698.5 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 = $5950
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5950 + ($5950 × 7% × 9)
= $5950 + ($5950 ×7/100 × 9)
= $5950 + (5950 × 7 × 9/100)
= $5950 + (41650 × 9/100)
= $5950 + (374850/100)
= $5950 + $3748.5 = $9698.5
Thus, Amount (A) to be paid = $9698.5 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 $5950, the simple interest in 1 year
= 7/100 × 5950
= 7 × 5950/100
= 41650/100 = $416.5
Thus, simple interest for 1 year = $416.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $416.5 × 9 = $3748.5
Thus, Simple Interest (SI) = $3748.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $3748.5
= $9698.5
Thus, Amount to be paid = $9698.5 Answer
Similar Questions
(1) Emily had to pay $5177.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.
(3) 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.
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
(5) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(6) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.
(8) If Jennifer paid $3900 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
(10) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.