Question:
What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?
Correct Answer
$4810
Solution And Explanation
Solution
Given,
Principal (P) = $3700
Rate of Simple Interest (SI) = 5%
Time (t) = 6 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% × 6
= $3700 ×5/100 × 6
= 3700 × 5 × 6/100
= 18500 × 6/100
= 111000/100
= $1110
Thus, Simple Interest = $1110
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 + $1110
= $4810
Thus, Amount to be paid = $4810 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) = 6 years
Thus, Amount (A)
= $3700 + ($3700 × 5% × 6)
= $3700 + ($3700 ×5/100 × 6)
= $3700 + (3700 × 5 × 6/100)
= $3700 + (18500 × 6/100)
= $3700 + (111000/100)
= $3700 + $1110 = $4810
Thus, Amount (A) to be paid = $4810 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 6 years
= Simple interest for 1 year × 6
= $185 × 6 = $1110
Thus, Simple Interest (SI) = $1110
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3700 + $1110
= $4810
Thus, Amount to be paid = $4810 Answer
Similar Questions
(1) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 3% simple interest?
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.
(3) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 4 years.
(5) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(6) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(7) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(8) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.