Question:
If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$4004
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 2%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $3850 × 2% × 2
= $3850 ×2/100 × 2
= 3850 × 2 × 2/100
= 7700 × 2/100
= 15400/100
= $154
Thus, Simple Interest = $154
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 = $3850 + $154
= $4004
Thus, Amount to be paid = $4004 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 = $3850
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 2 years
Thus, Amount (A)
= $3850 + ($3850 × 2% × 2)
= $3850 + ($3850 ×2/100 × 2)
= $3850 + (3850 × 2 × 2/100)
= $3850 + (7700 × 2/100)
= $3850 + (15400/100)
= $3850 + $154 = $4004
Thus, Amount (A) to be paid = $4004 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest in 1 year = $2
∴ For $1, the simple interest in 1 year = 2/100
∴ For $3850, the simple interest in 1 year
= 2/100 × 3850
= 2 × 3850/100
= 7700/100 = $77
Thus, simple interest in 1 year = $77
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $77 × 2 = $154
Thus, Simple Interest (SI) = $154
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $154
= $4004
Thus, Amount to be paid = $4004 Answer
Similar Questions
(1) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 6% simple interest?
(2) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?
(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.
(4) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(5) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 4 years.
(7) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(8) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(9) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.