Simple Interest
Math MCQs

Question :    Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5200

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

Amount (A) = $8476

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 = $8476 – $5200 = $3276

Thus, Simple Interest = $3276

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 × 3276}/_{5200 × 9}

= ³²⁷⁶⁰⁰/₄₆₈₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $5200

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

Simple Interest = $3276 (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 $5200

= ⁹/₁₀₀ × 5200

= ^{9 × 5200}/₁₀₀

= ⁴⁶⁸⁰⁰/₁₀₀ = 468

Thus, simple Interest for 1 year = $468

Now,

∵ If the simple Interest is $468, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₈ years

∴ If the simple Interest is $3276, then the time = ¹/₄₆₈ × 3276 years

= ^{1 × 3276}/₄₆₈ years

= ³²⁷⁶/₄₆₈ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 5% simple interest?

(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.

(3) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(4) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.

(5) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(6) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?

(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.

(8) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.

(10) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?