Simple Interest
Math MCQs

Question :    Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7560 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) = 10% per annum

Amount (A) = $7560

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 = $7560 – $4200 = $3360

Thus, Simple Interest = $3360

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 × 3360}/_{4200 × 10}

= ³³⁶⁰⁰⁰/₄₂₀₀₀

= 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) = 10% per annum

Simple Interest = $3360 (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 = 10% of Principal

= 10% of $4200

= ¹⁰/₁₀₀ × 4200

= ^{10 × 4200}/₁₀₀

= ⁴²⁰⁰⁰/₁₀₀ = 420

Thus, simple Interest for 1 year = $420

Now,

∵ If the simple Interest is $420, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₀ years

∴ If the simple Interest is $3360, then the time = ¹/₄₂₀ × 3360 years

= ^{1 × 3360}/₄₂₀ years

= ³³⁶⁰/₄₂₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 6% simple interest?

(2) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?

(4) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 3 years.

(6) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 2% simple interest?

(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 7 years.

(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.

(9) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.

(10) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 4 years.