Question:
What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?
Correct Answer
$4197.5
Solution And Explanation
Solution
Given,
Principal (P) = $3650
Rate of Simple Interest (SI) = 3%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 5
= $3650 ×3/100 × 5
= 3650 × 3 × 5/100
= 10950 × 5/100
= 54750/100
= $547.5
Thus, Simple Interest = $547.5
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 = $3650 + $547.5
= $4197.5
Thus, Amount to be paid = $4197.5 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 = $3650
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 5 years
Thus, Amount (A)
= $3650 + ($3650 × 3% × 5)
= $3650 + ($3650 ×3/100 × 5)
= $3650 + (3650 × 3 × 5/100)
= $3650 + (10950 × 5/100)
= $3650 + (54750/100)
= $3650 + $547.5 = $4197.5
Thus, Amount (A) to be paid = $4197.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3650, the simple interest in 1 year
= 3/100 × 3650
= 3 × 3650/100
= 10950/100 = $109.5
Thus, simple interest for 1 year = $109.5
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $109.5 × 5 = $547.5
Thus, Simple Interest (SI) = $547.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3650 + $547.5
= $4197.5
Thus, Amount to be paid = $4197.5 Answer
Similar Questions
(1) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?
(2) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.
(3) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 8 years.
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 4 years.
(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 4 years.
(7) Kenneth had to pay $5300 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?
(9) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if James borrowed a sum of $3000 at a 8% simple interest?