Simple Interest
Math MCQs

Question :    Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5200

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $7072

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 = $7072 – $5200 = $1872

Thus, Simple Interest = $1872

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 × 1872}/_{5200 × 6}

= ¹⁸⁷²⁰⁰/₃₁₂₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $5200

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $1872 (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 = 6% of Principal

= 6% of $5200

= ⁶/₁₀₀ × 5200

= ^{6 × 5200}/₁₀₀

= ³¹²⁰⁰/₁₀₀ = 312

Thus, simple Interest for 1 year = $312

Now,

∵ If the simple Interest is $312, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₁₂ years

∴ If the simple Interest is $1872, then the time = ¹/₃₁₂ × 1872 years

= ^{1 × 1872}/₃₁₂ years

= ¹⁸⁷²/₃₁₂ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.

(2) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 8 years.

(3) How much loan did Nancy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6765 to clear it?

(4) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?

(5) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 2% simple interest?

(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.

(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.

(8) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.

(9) How much loan did Ronald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9375 to clear it?

(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.