Simple Interest
Math MCQs

Question :    How much loan did Daniel borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7320 to clear it?

Correct Answer  $6100

Solution & Explanation

Solution

Given,

Amount (A) = $7320

Rate of Simple Interest (R) = 4%

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

$7320 = P (1 + 4% × 5)

⇒ $7320 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7320 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7320 = P (1 + ²⁰/₁₀₀)

⇒ $7320 = P (^{100 + 20}/₁₀₀)

⇒ $7320 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7320

⇒ P = ⁷³²⁰/_¹²⁰/100

⇒ P = 7320 × ¹⁰⁰/₁₂₀

⇒ P = ^{7320 × 100}/₁₂₀

⇒ P = ⁷³²⁰⁰⁰/₁₂₀

⇒ P = $6100

Thus, the sum borrowed (P) = $6100 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 7320, then the Principal = ¹⁰⁰/₁₂₀ × 7320

= ^{100 × 7320}/₁₂₀

= ⁷³²⁰⁰⁰/₁₂₀

= 6100

Thus, Principal = $6100

Thus, the sum borrowed = $6100 Answer

Similar Questions

(1) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 7% simple interest?

(2) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 4% simple interest?

(3) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?

(4) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.

(5) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 4 years.

(6) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.

(7) If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.

(9) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.