Simple Interest
Math MCQs

Question :    Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6258 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4200

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

Amount (A) = $6258

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 = $6258 – $4200 = $2058

Thus, Simple Interest = $2058

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 × 2058}/_{4200 × 7}

= ²⁰⁵⁸⁰⁰/₂₉₄₀₀

= 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) = $4200

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

Simple Interest = $2058 (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 $4200

= ⁷/₁₀₀ × 4200

= ^{7 × 4200}/₁₀₀

= ²⁹⁴⁰⁰/₁₀₀ = 294

Thus, simple Interest for 1 year = $294

Now,

∵ If the simple Interest is $294, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₉₄ years

∴ If the simple Interest is $2058, then the time = ¹/₂₉₄ × 2058 years

= ^{1 × 2058}/₂₉₄ years

= ²⁰⁵⁸/₂₉₄ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(2) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9060 to clear it?

(3) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?

(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.

(5) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.

(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.

(8) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.

(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?

(10) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?