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Mohan deposit certain amount in bank saving account for 6 year which give simple interest of x% annually and invest same principle in fix deposit for 2 year which gives interest rate 10% and compounded annually, total interest he get from saving account to fix deposit in the ratio of 6 : 7, if bank provide (x + 3)% rate annually on saving account deposit, then difference of interest arise Rs.7,500 between saving account and fix deposit after respective time period, what amount he invest in fix deposit?

Mohan deposit certain amount in bank saving account for 6 year which give simple interest of x% annually and invest same principle in fix deposit for 2 year which gives interest rate 10% and compounded annually, total interest he get from saving account to fix deposit in the ratio of 6 : 7, if bank provide (x + 3)% rate annually on saving account deposit, then difference of interest arise Rs.7,500 between saving account and fix deposit after respective time period, what amount he invest in fix deposit? Correct Answer Rs.50,000

Given:

Amount deposit in saving account = Amount deposit in fix deposit

Saving account on simple interest = x% annually

Period of time for which deposited in saving account = 6 year

Fix deposit on compound interest = 10% annually

Period of time for which deposited in fix deposit = 2 year

Total interest he get from saving account : Total interest get on fix deposit in the ratio of = 6 : 7

If bank provide (x + 3)% rate annually on saving account deposit, then difference of interest arise Rs.7,500 between saving account and fix deposit after respective time period

Concept:

When annually interest rate x% given for 2 year compound interest than effective interest for two year is = x + x + (x2/100)

When different interest getting on same principal, then amount of interest also in ratio of effective interest% ratio.

(Amount deposit in saving account = Amount deposit in fix deposit), means both deposit are 100% individually.

Calculation:

Effective simple interest on saving account for 6 year with x% interest rate = (6 × x)%

Effective compound interest on fix deposit for 2 year with 10% = 10 + 10 + (10 × 10)/100 = 21%

Total interest he get from saving account : Total interest get on fix deposit in the ratio of = 6x : 7x

∵ 7x = 21%

∴ 6x = 18% (effective interest for 6 year of simple interest)

Rate of interest for simple interest x% = 18/6 = 3%

If bank provide (x + 3)% rate annually on saving account deposit, then difference of interest arise Rs.7,500 between saving account and fix deposit after respective time period

Now, bank provide (3 + 3)% simple interest annually on saving account

⇒ New simple interest annually on saving account = 6%

Effective interest occur on saving account for 6 year = 6 × 6 = 36%

Difference of interest between saving account and fix deposit after respective time period = 36 – 21 = 15%

∵ Difference of interest arise Rs.7,500 = 15%

And Amount of Mohan invest in fix deposit = 100%

Amount of Mohan invest in fix deposit = (7,500/15) × 100

⇒ Rs.50,000

∴ Amount of Mohan invest in fix deposit is Rs.50,000

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