Simple Interest
Math MCQs

Question :    Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8568 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6300

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $8568

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 = $8568 – $6300 = $2268

Thus, Simple Interest = $2268

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 × 2268}/_{6300 × 6}

= ²²⁶⁸⁰⁰/₃₇₈₀₀

= 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) = $6300

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2268 (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 $6300

= ⁶/₁₀₀ × 6300

= ^{6 × 6300}/₁₀₀

= ³⁷⁸⁰⁰/₁₀₀ = 378

Thus, simple Interest for 1 year = $378

Now,

∵ If the simple Interest is $378, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₇₈ years

∴ If the simple Interest is $2268, then the time = ¹/₃₇₈ × 2268 years

= ^{1 × 2268}/₃₇₈ years

= ²²⁶⁸/₃₇₈ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 3 years.

(3) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5712 to clear the loan, then find the time period of the loan.

(4) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(5) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.

(6) If William paid $4060 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.

(10) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.