Question:
What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 5% simple interest?
Correct Answer
$4745
Solution And Explanation
Solution
Given,
Principal (P) = $3650
Rate of Simple Interest (SI) = 5%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 6
= $3650 ×5/100 × 6
= 3650 × 5 × 6/100
= 18250 × 6/100
= 109500/100
= $1095
Thus, Simple Interest = $1095
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 + $1095
= $4745
Thus, Amount to be paid = $4745 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) = 5%
And, Time (t) = 6 years
Thus, Amount (A)
= $3650 + ($3650 × 5% × 6)
= $3650 + ($3650 ×5/100 × 6)
= $3650 + (3650 × 5 × 6/100)
= $3650 + (18250 × 6/100)
= $3650 + (109500/100)
= $3650 + $1095 = $4745
Thus, Amount (A) to be paid = $4745 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3650, the simple interest in 1 year
= 5/100 × 3650
= 5 × 3650/100
= 18250/100 = $182.5
Thus, simple interest for 1 year = $182.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $182.5 × 6 = $1095
Thus, Simple Interest (SI) = $1095
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3650 + $1095
= $4745
Thus, Amount to be paid = $4745 Answer
Similar Questions
(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 3 years.
(2) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(3) If Donna paid $5626 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(5) If Anthony paid $4644 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) If Linda paid $4020 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.
(8) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(9) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.