Question

A bank advertises that it compounds money quarterly and that it will take Double your money in 10 years. what is the interest-rate?

Answer 1

The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.

Explanation:

The given is,

Compounds money quarterly

Double your money in 10 years

Step:1

Formula to calculate future investment with compounded quarterly,

`A =P(1+(r)/(n) )^(nt)`...............................(1)

Where, A - Future amount

P - Initial investment\

r - Rate of interest

n - No. of compounding in a year

t - No. of years

Step:2

Let, P = X

A = 2X ( Double your money )

From given, n - 4 ( for compounding quarterly )

t - 10 years

From equation (1)

`2X =X(1+(r)/(4) )^((4)(10))`

`(2X)/(X) =(1+(r)/(4) )^((4)(10))`

`2 =(1+(r)/(4) )^(40)`

Take root
`40^(th)` root on both side,

`\sqrt[40]{2} = (1+(r)/(4) )`

`1.017479692 = ((4+r)/(4) )`

`(1.017479692)(4) = (r+4)`

`4.06992=(r+4)`

`r = 4.06992 -4`

`r =( 0.06992)(100)`

r = 6.992 %

Result:

The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.