Simple Interest
Math MCQs

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

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4800

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $6816

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 = $6816 – $4800 = $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}/_{4800 × 7}

= ²⁰¹⁶⁰⁰/₃₃₆₀₀

= 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) = $4800

Rate of Simple Interest (R) = 7% 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 = 7% of Principal

= 7% of $4800

= ⁷/₁₀₀ × 4800

= ^{7 × 4800}/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 $2016, then the time = ¹/₃₃₆ × 2016 years

= ^{1 × 2016}/₃₃₆ years

= ²⁰¹⁶/₃₃₆ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.

(2) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 10% simple interest?

(3) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.

(4) How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?

(5) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?

(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.

(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.

(8) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.

(9) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?

(10) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.