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 $9176 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6200

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

Amount (A) = $9176

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 = $9176 – $6200 = $2976

Thus, Simple Interest = $2976

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 × 2976}/_{6200 × 6}

= ²⁹⁷⁶⁰⁰/₃₇₂₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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 = $2976 (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 $2976, then the time = ¹/₃₇₂ × 2976 years

= ^{1 × 2976}/₃₇₂ years

= ²⁹⁷⁶/₃₇₂ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.

(2) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.

(3) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 7% simple interest?

(5) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.

(6) If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?

(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 7 years.

(9) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(10) What amount does John have to pay after 5 years if he takes a loan of $3200 at 4% simple interest?