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) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 5% simple interest?

(2) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?

(3) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?

(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 4 years.

(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 3% simple interest?

(6) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.

(7) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) 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.

(9) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.

(10) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.