Simple Interest
Math MCQs

Question :    If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3550

Solution & Explanation

Solution

Given,

Amount (A) = $4260

Rate of Simple Interest (R) = 5%

Time (T) = 4 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$4260 = P (1 + 5% × 4)

⇒ $4260 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4260 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4260 = P (1 + ²⁰/₁₀₀)

⇒ $4260 = P (^{100 + 20}/₁₀₀)

⇒ $4260 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4260

⇒ P = ⁴²⁶⁰/_¹²⁰/100

⇒ P = 4260 × ¹⁰⁰/₁₂₀

⇒ P = ^{4260 × 100}/₁₂₀

⇒ P = ⁴²⁶⁰⁰⁰/₁₂₀

⇒ P = $3550

Thus, the sum borrowed (P) = $3550 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 5 = 20

Thus, simple interest for 4 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 4260, then the Principal = ¹⁰⁰/₁₂₀ × 4260

= ^{100 × 4260}/₁₂₀

= ⁴²⁶⁰⁰⁰/₁₂₀

= 3550

Thus, Principal = $3550

Thus, the sum borrowed = $3550 Answer

Similar Questions

(1) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?

(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.

(3) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) 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.

(5) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.

(7) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.

(8) If Robert borrowed $3100 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?

(10) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.