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) If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(2) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 3 years.
(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 3 years.
(5) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?
(7) 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.
(8) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(9) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 4% simple interest?
(10) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.