Simple Interest
Math MCQs

Question :    Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6200

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $9548

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 = $9548 – $6200 = $3348

Thus, Simple Interest = $3348

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 × 3348}/_{6200 × 9}

= ³³⁴⁸⁰⁰/₅₅₈₀₀

= 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) = $6200

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $3348 (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 = 9% of Principal

= 9% of $6200

= ⁹/₁₀₀ × 6200

= ^{9 × 6200}/₁₀₀

= ⁵⁵⁸⁰⁰/₁₀₀ = 558

Thus, simple Interest for 1 year = $558

Now,

∵ If the simple Interest is $558, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₅₈ years

∴ If the simple Interest is $3348, then the time = ¹/₅₅₈ × 3348 years

= ^{1 × 3348}/₅₅₈ years

= ³³⁴⁸/₅₅₈ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.

(2) How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?

(3) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.

(4) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?

(5) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.

(7) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.

(8) If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?

(10) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.