Question

How much money should be deposited today in an account that earns 3 % compounded semiannually so that it will accumulate to $ 8000 in three​ years?

Answer 1

The amount of money which should be deposited is $ 7316.627

Explanation:

Given as :

Let the principal = p

The interest rate compounded semiannually = 3 %

Time period = 3 years

The amount after three years = A = $ 8000

Now, Amount = Principal ×
`(1 +(Rate)/(2* 100))^(2* Time)`

Or, $ 8000 = Principal ×
`(1 +(3)/(2* 100))^(2* 3)`

Or, $ 8000 = p ×
`((203)/(200))^(6)`

Or, p =
`(8000)/(1.0934)`

∴ p = $ 7316.627

Hence The amount of money which should be deposited is $ 7316.627 Answer