Simple Interest
Math MCQs

Question :    Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7526 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) = 6% per annum

Amount (A) = $7526

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 = $7526 – $5300 = $2226

Thus, Simple Interest = $2226

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 × 2226}/_{5300 × 6}

= ²²²⁶⁰⁰/₃₁₈₀₀

= 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) = 6% per annum

Simple Interest = $2226 (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 = 6% of Principal

= 6% of $5300

= ⁶/₁₀₀ × 5300

= ^{6 × 5300}/₁₀₀

= ³¹⁸⁰⁰/₁₀₀ = 318

Thus, simple Interest for 1 year = $318

Now,

∵ If the simple Interest is $318, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₁₈ years

∴ If the simple Interest is $2226, then the time = ¹/₃₁₈ × 2226 years

= ^{1 × 2226}/₃₁₈ years

= ²²²⁶/₃₁₈ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.

(2) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.

(4) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.

(5) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 3% simple interest?

(6) If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

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

(8) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?

(9) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?

(10) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.