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) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.
(2) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(4) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.
(5) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(6) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(7) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 7 years.
(9) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(10) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.