Simple Interest
Math MCQs

Question :  ( 1 of 10 )  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.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5300

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

Amount (A) = $9010

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 = $9010 – $5300 = $3710

Thus, Simple Interest = $3710

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 × 3710}/_{5300 × 7}

= ³⁷¹⁰⁰⁰/₃₇₁₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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 = $3710 (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 $3710, then the time = ¹/₃₇₁ × 3710 years

= ^{1 × 3710}/₃₇₁ years

= ³⁷¹⁰/₃₇₁ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.

(3) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 7% simple interest?

(5) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?

(6) How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?

(7) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.

(8) Joseph had to pay $4144 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.

(10) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 2% simple interest?