Question:
What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?
Correct Answer
$5621
Solution And Explanation
Solution
Given,
Principal (P) = $3650
Rate of Simple Interest (SI) = 9%
Time (t) = 6 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) = $3650 × 9% × 6
= $3650 ×9/100 × 6
= 3650 × 9 × 6/100
= 32850 × 6/100
= 197100/100
= $1971
Thus, Simple Interest = $1971
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 = $3650 + $1971
= $5621
Thus, Amount to be paid = $5621 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 = $3650
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 6 years
Thus, Amount (A)
= $3650 + ($3650 × 9% × 6)
= $3650 + ($3650 ×9/100 × 6)
= $3650 + (3650 × 9 × 6/100)
= $3650 + (32850 × 6/100)
= $3650 + (197100/100)
= $3650 + $1971 = $5621
Thus, Amount (A) to be paid = $5621 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 $3650, the simple interest in 1 year
= 9/100 × 3650
= 9 × 3650/100
= 32850/100 = $328.5
Thus, simple interest for 1 year = $328.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $328.5 × 6 = $1971
Thus, Simple Interest (SI) = $1971
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3650 + $1971
= $5621
Thus, Amount to be paid = $5621 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(2) If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 4 years.
(4) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 to clear the loan, then find the time period of the loan.
(5) 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.
(6) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.
(8) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(9) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(10) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7344 to clear the loan, then find the time period of the loan.