Question:
Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 4 years.
Correct Answer
$4380
Solution And Explanation
Solution
Given,
Principal (P) = $3650
Rate of Simple Interest (SI) = 5%
Time (t) = 4 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% × 4
= $3650 ×5/100 × 4
= 3650 × 5 × 4/100
= 18250 × 4/100
= 73000/100
= $730
Thus, Simple Interest = $730
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 + $730
= $4380
Thus, Amount to be paid = $4380 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) = 4 years
Thus, Amount (A)
= $3650 + ($3650 × 5% × 4)
= $3650 + ($3650 ×5/100 × 4)
= $3650 + (3650 × 5 × 4/100)
= $3650 + (18250 × 4/100)
= $3650 + (73000/100)
= $3650 + $730 = $4380
Thus, Amount (A) to be paid = $4380 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 4 years
= Simple interest for 1 year × 4
= $182.5 × 4 = $730
Thus, Simple Interest (SI) = $730
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3650 + $730
= $4380
Thus, Amount to be paid = $4380 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
(2) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.
(3) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.
(5) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?
(6) Jessica had to pay $4312.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.
(8) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
(9) Sarah had to pay $4312 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Andrew had to pay $5232 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.