Simple Interest
MCQs Math

Question:     Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8432 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution And Explanation

Solution

Given,

Principal (P) = $6200

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

Amount (A) = $8432

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 = $8432 – $6200 = $2232

Thus, Simple Interest = $2232

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 × 2232}/_{6200 × 6}

= ²²³²⁰⁰/₃₇₂₀₀

= 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) = 6% per annum

Simple Interest = $2232 (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 $6200

= ⁶/₁₀₀ × 6200

= ^{6 × 6200}/₁₀₀

= ³⁷²⁰⁰/₁₀₀ = 372

Thus, simple Interest for 1 year = $372

Now,

∵ If the simple Interest is $372, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₇₂ years

∴ If the simple Interest is $2232, then the time = ¹/₃₇₂ × 2232 years

= ^{1 × 2232}/₃₇₂ years

= ²²³²/₃₇₂ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?

(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 4 years.

(3) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?

(4) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.

(6) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?

(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.

(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?

(9) If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 7 years.