Simple Interest
Math MCQs

Question :    How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?

Correct Answer  $5350

Solution & Explanation

Solution

Given,

Amount (A) = $6152.5

Rate of Simple Interest (R) = 3%

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

$6152.5 = P (1 + 3% × 5)

⇒ $6152.5 = P (1 + ³/₁₀₀ × 5)

⇒ $6152.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6152.5 = P (1 + ¹⁵/₁₀₀)

⇒ $6152.5 = P (^{100 + 15}/₁₀₀)

⇒ $6152.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6152.5

⇒ P = ^6152.5/_¹¹⁵/100

⇒ P = 6152.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{6152.5 × 100}/₁₁₅

⇒ P = ⁶¹⁵²⁵⁰/₁₁₅

⇒ P = $5350

Thus, the sum borrowed (P) = $5350 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 6152.5, then the Principal = ¹⁰⁰/₁₁₅ × 6152.5

= ^{100 × 6152.5}/₁₁₅

= ⁶¹⁵²⁵⁰/₁₁₅

= 5350

Thus, Principal = $5350

Thus, the sum borrowed = $5350 Answer

Similar Questions

(1) Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.

(3) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?

(4) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?

(5) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 3 years.

(6) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.

(7) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.

(8) How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?

(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?

(10) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.