Simple Interest
Math MCQs

Question :    How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?

Correct Answer  $7350

Solution & Explanation

Solution

Given,

Amount (A) = $9187.5

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

$9187.5 = P (1 + 5% × 5)

⇒ $9187.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9187.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9187.5 = P (1 + ²⁵/₁₀₀)

⇒ $9187.5 = P (^{100 + 25}/₁₀₀)

⇒ $9187.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9187.5

⇒ P = ^9187.5/_¹²⁵/100

⇒ P = 9187.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{9187.5 × 100}/₁₂₅

⇒ P = ⁹¹⁸⁷⁵⁰/₁₂₅

⇒ P = $7350

Thus, the sum borrowed (P) = $7350 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 9187.5, then the Principal = ¹⁰⁰/₁₂₅ × 9187.5

= ^{100 × 9187.5}/₁₂₅

= ⁹¹⁸⁷⁵⁰/₁₂₅

= 7350

Thus, Principal = $7350

Thus, the sum borrowed = $7350 Answer

Similar Questions

(1) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 3 years.

(2) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?

(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.

(4) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?

(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 3 years.

(6) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 8% simple interest?

(7) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 4 years.

(9) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?

(10) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 7 years.