Simple Interest
Math MCQs

Question :    Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7897 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5300

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

Amount (A) = $7897

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 = $7897 – $5300 = $2597

Thus, Simple Interest = $2597

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 × 2597}/_{5300 × 7}

= ²⁵⁹⁷⁰⁰/₃₇₁₀₀

= 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) = $5300

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

Simple Interest = $2597 (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 $5300

= ⁷/₁₀₀ × 5300

= ^{7 × 5300}/₁₀₀

= ³⁷¹⁰⁰/₁₀₀ = 371

Thus, simple Interest for 1 year = $371

Now,

∵ If the simple Interest is $371, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₇₁ years

∴ If the simple Interest is $2597, then the time = ¹/₃₇₁ × 2597 years

= ^{1 × 2597}/₃₇₁ years

= ²⁵⁹⁷/₃₇₁ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?

(2) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.

(4) How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?

(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?

(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 8 years.

(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.

(8) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(9) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?

(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.