Simple Interest
Math MCQs

Question :    Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4200

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

Amount (A) = $7224

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 = $7224 – $4200 = $3024

Thus, Simple Interest = $3024

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 × 3024}/_{4200 × 8}

= ³⁰²⁴⁰⁰/₃₃₆₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $4200

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

Simple Interest = $3024 (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 $4200

= ⁸/₁₀₀ × 4200

= ^{8 × 4200}/₁₀₀

= ³³⁶⁰⁰/₁₀₀ = 336

Thus, simple Interest for 1 year = $336

Now,

∵ If the simple Interest is $336, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₃₆ years

∴ If the simple Interest is $3024, then the time = ¹/₃₃₆ × 3024 years

= ^{1 × 3024}/₃₃₆ years

= ³⁰²⁴/₃₃₆ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?

(2) Mary had to pay $3324.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?

(4) If Susan borrowed $3650 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.

(6) If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?

(8) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 8% simple interest?

(9) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?

(10) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.