Question:
What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 10% simple interest?
Correct Answer
$5760
Solution And Explanation
Solution
Given,
Principal (P) = $3600
Rate of Simple Interest (SI) = 10%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $3600 × 10% × 6
= $3600 ×10/100 × 6
= 3600 × 10 × 6/100
= 36000 × 6/100
= 216000/100
= $2160
Thus, Simple Interest = $2160
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 = $3600 + $2160
= $5760
Thus, Amount to be paid = $5760 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 = $3600
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 6 years
Thus, Amount (A)
= $3600 + ($3600 × 10% × 6)
= $3600 + ($3600 ×10/100 × 6)
= $3600 + (3600 × 10 × 6/100)
= $3600 + (36000 × 6/100)
= $3600 + (216000/100)
= $3600 + $2160 = $5760
Thus, Amount (A) to be paid = $5760 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3600, the simple interest in 1 year
= 10/100 × 3600
= 10 × 3600/100
= 36000/100 = $360
Thus, simple interest for 1 year = $360
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $360 × 6 = $2160
Thus, Simple Interest (SI) = $2160
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3600 + $2160
= $5760
Thus, Amount to be paid = $5760 Answer
Similar Questions
(1) If Kenneth paid $5800 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 4 years.
(3) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 4% simple interest?
(4) How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?
(5) Emily had to pay $5177.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?
(8) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(9) How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?
(10) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.