Simple Interest
Math MCQs

Question :    How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?

Correct Answer  $5650

Solution & Explanation

Solution

Given,

Amount (A) = $6497.5

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

$6497.5 = P (1 + 3% × 5)

⇒ $6497.5 = P (1 + ³/₁₀₀ × 5)

⇒ $6497.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6497.5 = P (1 + ¹⁵/₁₀₀)

⇒ $6497.5 = P (^{100 + 15}/₁₀₀)

⇒ $6497.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6497.5

⇒ P = ^6497.5/_¹¹⁵/100

⇒ P = 6497.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{6497.5 × 100}/₁₁₅

⇒ P = ⁶⁴⁹⁷⁵⁰/₁₁₅

⇒ P = $5650

Thus, the sum borrowed (P) = $5650 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 6497.5, then the Principal = ¹⁰⁰/₁₁₅ × 6497.5

= ^{100 × 6497.5}/₁₁₅

= ⁶⁴⁹⁷⁵⁰/₁₁₅

= 5650

Thus, Principal = $5650

Thus, the sum borrowed = $5650 Answer

Similar Questions

(1) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?

(2) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.

(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 2% simple interest?

(4) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?

(5) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 4% simple interest.

(6) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.

(7) How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?

(8) How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?

(9) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6854 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.