Question:
Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
Correct Answer
$8320
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 6%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5200 × 6% × 10
= $5200 ×6/100 × 10
= 5200 × 6 × 10/100
= 31200 × 10/100
= 312000/100
= $3120
Thus, Simple Interest = $3120
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 = $5200 + $3120
= $8320
Thus, Amount to be paid = $8320 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 = $5200
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5200 + ($5200 × 6% × 10)
= $5200 + ($5200 ×6/100 × 10)
= $5200 + (5200 × 6 × 10/100)
= $5200 + (31200 × 10/100)
= $5200 + (312000/100)
= $5200 + $3120 = $8320
Thus, Amount (A) to be paid = $8320 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5200, the simple interest in 1 year
= 6/100 × 5200
= 6 × 5200/100
= 31200/100 = $312
Thus, simple interest for 1 year = $312
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $312 × 10 = $3120
Thus, Simple Interest (SI) = $3120
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $3120
= $8320
Thus, Amount to be paid = $8320 Answer
Similar Questions
(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 3 years.
(2) If Susan borrowed $3650 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(4) How much loan did Donna borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7535 to clear it?
(5) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 7% simple interest.
(6) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(7) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.
(8) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?
(9) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?
(10) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?