Simple Interest
Math MCQs

Question :    Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5700

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $9120

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 = $9120 – $5700 = $3420

Thus, Simple Interest = $3420

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 × 3420}/_{5700 × 10}

= ³⁴²⁰⁰⁰/₅₇₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $5700

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $3420 (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 $5700

= ¹⁰/₁₀₀ × 5700

= ^{10 × 5700}/₁₀₀

= ⁵⁷⁰⁰⁰/₁₀₀ = 570

Thus, simple Interest for 1 year = $570

Now,

∵ If the simple Interest is $570, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₇₀ years

∴ If the simple Interest is $3420, then the time = ¹/₅₇₀ × 3420 years

= ^{1 × 3420}/₅₇₀ years

= ³⁴²⁰/₅₇₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.

(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 7 years.

(3) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?

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

(5) Paul had to pay $5264 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) If Daniel paid $4756 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.

(8) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?

(9) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.

(10) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 8% simple interest?