Question:
What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 5% simple interest?
Correct Answer
$4625
Solution And Explanation
Solution
Given,
Principal (P) = $3700
Rate of Simple Interest (SI) = 5%
Time (t) = 5 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) = $3700 × 5% × 5
= $3700 ×5/100 × 5
= 3700 × 5 × 5/100
= 18500 × 5/100
= 92500/100
= $925
Thus, Simple Interest = $925
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 = $3700 + $925
= $4625
Thus, Amount to be paid = $4625 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 = $3700
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 5 years
Thus, Amount (A)
= $3700 + ($3700 × 5% × 5)
= $3700 + ($3700 ×5/100 × 5)
= $3700 + (3700 × 5 × 5/100)
= $3700 + (18500 × 5/100)
= $3700 + (92500/100)
= $3700 + $925 = $4625
Thus, Amount (A) to be paid = $4625 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 $3700, the simple interest in 1 year
= 5/100 × 3700
= 5 × 3700/100
= 18500/100 = $185
Thus, simple interest for 1 year = $185
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $185 × 5 = $925
Thus, Simple Interest (SI) = $925
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3700 + $925
= $4625
Thus, Amount to be paid = $4625 Answer
Similar Questions
(1) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(4) If Karen paid $4266 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
(6) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 3 years.
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 8 years.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.