Simple Interest
Math MCQs

Question :    Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 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) = 8% per annum

Amount (A) = $11160

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 = $11160 – $6200 = $4960

Thus, Simple Interest = $4960

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 × 4960}/_{6200 × 8}

= ⁴⁹⁶⁰⁰⁰/₄₉₆₀₀

= 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) = 8% per annum

Simple Interest = $4960 (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 = 8% of Principal

= 8% of $6200

= ⁸/₁₀₀ × 6200

= ^{8 × 6200}/₁₀₀

= ⁴⁹⁶⁰⁰/₁₀₀ = 496

Thus, simple Interest for 1 year = $496

Now,

∵ If the simple Interest is $496, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₉₆ years

∴ If the simple Interest is $4960, then the time = ¹/₄₉₆ × 4960 years

= ^{1 × 4960}/₄₉₆ years

= ⁴⁹⁶⁰/₄₉₆ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.

(2) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.

(3) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?

(4) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 9% simple interest?

(5) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 7% simple interest?

(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 3% simple interest?

(7) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.

(8) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 6% simple interest?

(9) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.

(10) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.