Simple Interest
Math MCQs

Question :    How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?

Correct Answer  $5950

Solution & Explanation

Solution

Given,

Amount (A) = $7437.5

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

$7437.5 = P (1 + 5% × 5)

⇒ $7437.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7437.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7437.5 = P (1 + ²⁵/₁₀₀)

⇒ $7437.5 = P (^{100 + 25}/₁₀₀)

⇒ $7437.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7437.5

⇒ P = ^7437.5/_¹²⁵/100

⇒ P = 7437.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{7437.5 × 100}/₁₂₅

⇒ P = ⁷⁴³⁷⁵⁰/₁₂₅

⇒ P = $5950

Thus, the sum borrowed (P) = $5950 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 7437.5, then the Principal = ¹⁰⁰/₁₂₅ × 7437.5

= ^{100 × 7437.5}/₁₂₅

= ⁷⁴³⁷⁵⁰/₁₂₅

= 5950

Thus, Principal = $5950

Thus, the sum borrowed = $5950 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.

(2) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.

(3) If Sarah paid $4466 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 8% simple interest?

(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?

(6) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.

(7) Robert had to pay $3472 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.

(10) What amount does John have to pay after 5 years if he takes a loan of $3200 at 4% simple interest?