Simple Interest
Math MCQs

Question :    How much loan did Barbara borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6937.5 to clear it?

Correct Answer  $5550

Solution & Explanation

Solution

Given,

Amount (A) = $6937.5

Rate of Simple Interest (R) = 5%

Time (T) = 5 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

$6937.5 = P (1 + 5% × 5)

⇒ $6937.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6937.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6937.5 = P (1 + ²⁵/₁₀₀)

⇒ $6937.5 = P (^{100 + 25}/₁₀₀)

⇒ $6937.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6937.5

⇒ P = ^6937.5/_¹²⁵/100

⇒ P = 6937.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{6937.5 × 100}/₁₂₅

⇒ P = ⁶⁹³⁷⁵⁰/₁₂₅

⇒ P = $5550

Thus, the sum borrowed (P) = $5550 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 6937.5, then the Principal = ¹⁰⁰/₁₂₅ × 6937.5

= ^{100 × 6937.5}/₁₂₅

= ⁶⁹³⁷⁵⁰/₁₂₅

= 5550

Thus, Principal = $5550

Thus, the sum borrowed = $5550 Answer

Similar Questions

(1) Emily had to pay $5320 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?

(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 7% simple interest?

(4) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 3 years.

(5) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?

(6) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?

(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.

(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.

(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?

(10) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?