Simple Interest
Math MCQs

Question :  ( 1 of 10 )  Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6300

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $11340

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $11340 – $6300 = $5040

Thus, Simple Interest = $5040

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 5040}/_{6300 × 8}

= ⁵⁰⁴⁰⁰⁰/₅₀₄₀₀

= 10 years (using formula)

Thus, Time (T) = 10 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $6300

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $5040 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 8% of Principal

= 8% of $6300

= ⁸/₁₀₀ × 6300

= ^{8 × 6300}/₁₀₀

= ⁵⁰⁴⁰⁰/₁₀₀ = 504

Thus, simple Interest for 1 year = $504

Now,

∵ If the simple Interest is $504, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₀₄ years

∴ If the simple Interest is $5040, then the time = ¹/₅₀₄ × 5040 years

= ^{1 × 5040}/₅₀₄ years

= ⁵⁰⁴⁰/₅₀₄ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) In how much time a principal of $3150 will amount to $3402 at a simple interest of 2% per annum?

(2) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.

(3) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 9% simple interest.

(4) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $13000 to clear the loan, then find the time period of the loan.

(5) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11946 to clear the loan, then find the time period of the loan.

(6) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.

(7) In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?

(8) What amount will be due after 2 years if James borrowed a sum of $3000 at a 10% simple interest?

(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?

(10) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.