Simple Interest
Math MCQs

Question :    David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4800

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

Amount (A) = $7488

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 = $7488 – $4800 = $2688

Thus, Simple Interest = $2688

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 × 2688}/_{4800 × 8}

= ²⁶⁸⁸⁰⁰/₃₈₄₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = 8% per annum

Simple Interest = $2688 (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 $4800

= ⁸/₁₀₀ × 4800

= ^{8 × 4800}/₁₀₀

= ³⁸⁴⁰⁰/₁₀₀ = 384

Thus, simple Interest for 1 year = $384

Now,

∵ If the simple Interest is $384, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₈₄ years

∴ If the simple Interest is $2688, then the time = ¹/₃₈₄ × 2688 years

= ^{1 × 2688}/₃₈₄ years

= ²⁶⁸⁸/₃₈₄ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?

(2) If Elizabeth paid $4002 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 8 years.

(4) If James borrowed $3000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(5) How much loan did Donna borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8220 to clear it?

(6) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?

(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 7 years.

(9) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.

(10) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.