Simple Interest
Math MCQs

Question :    How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?

Correct Answer  $5700

Solution & Explanation

Solution

Given,

Amount (A) = $6555

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

$6555 = P (1 + 3% × 5)

⇒ $6555 = P (1 + ³/₁₀₀ × 5)

⇒ $6555 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6555 = P (1 + ¹⁵/₁₀₀)

⇒ $6555 = P (^{100 + 15}/₁₀₀)

⇒ $6555 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6555

⇒ P = ⁶⁵⁵⁵/_¹¹⁵/100

⇒ P = 6555 × ¹⁰⁰/₁₁₅

⇒ P = ^{6555 × 100}/₁₁₅

⇒ P = ⁶⁵⁵⁵⁰⁰/₁₁₅

⇒ P = $5700

Thus, the sum borrowed (P) = $5700 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 6555, then the Principal = ¹⁰⁰/₁₁₅ × 6555

= ^{100 × 6555}/₁₁₅

= ⁶⁵⁵⁵⁰⁰/₁₁₅

= 5700

Thus, Principal = $5700

Thus, the sum borrowed = $5700 Answer

Similar Questions

(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.

(2) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 9% simple interest?

(3) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.

(4) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.

(5) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?

(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 2% simple interest?

(7) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

(8) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?

(9) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?

(10) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?