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

Answer:

The amount of money which should be deposited is $ 7316.627

Step-by-step 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 × $(1 +\frac{Rate}{2\times 100})^{2\times Time}$

Or,      $ 8000 = Principal × $(1 +\frac{3}{2\times 100})^{2\times 3}$

Or,      $ 8000 = p × $(\frac{203}{200})^{6}$

Or,      p = $\frac{8000}{1.0934}$

∴         p = $ 7316.627  

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