Simple Interest
Math MCQs

Question :    Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6200

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

Amount (A) = $9920

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 = $9920 – $6200 = $3720

Thus, Simple Interest = $3720

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 × 3720}/_{6200 × 6}

= ³⁷²⁰⁰⁰/₃₇₂₀₀

= 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) = $6200

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

Simple Interest = $3720 (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 $3720, then the time = ¹/₃₇₂ × 3720 years

= ^{1 × 3720}/₃₇₂ years

= ³⁷²⁰/₃₇₂ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.

(2) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?

(3) In how much time a principal of $3200 will amount to $3584 at a simple interest of 4% per annum?

(4) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.

(5) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 9% simple interest?

(6) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?

(7) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.

(8) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.

(9) Linda had to pay $3752 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) 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.