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) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.
(2) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.
(3) Lisa had to pay $4293 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.
(5) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?
(6) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(7) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(8) How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?
(9) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(10) If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.