Simple Interest
Math MCQs

Question :  ( 1 of 10 )  Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4200

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

Amount (A) = $6216

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 = $6216 – $4200 = $2016

Thus, Simple Interest = $2016

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 × 2016}/_{4200 × 6}

= ²⁰¹⁶⁰⁰/₂₅₂₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = 6% per annum

Simple Interest = $2016 (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 $4200

= ⁶/₁₀₀ × 4200

= ^{6 × 4200}/₁₀₀

= ²⁵²⁰⁰/₁₀₀ = 252

Thus, simple Interest for 1 year = $252

Now,

∵ If the simple Interest is $252, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₅₂ years

∴ If the simple Interest is $2016, then the time = ¹/₂₅₂ × 2016 years

= ^{1 × 2016}/₂₅₂ years

= ²⁰¹⁶/₂₅₂ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?

(2) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?

(3) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

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

(5) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.

(6) In how much time a principal of $3100 will amount to $3348 at a simple interest of 2% per annum?

(7) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.

(8) If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) If Joseph paid $4144 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 3 years.