Question

If you would like to accumulate 7,500 over the next 5 years, how much must you deposit each six months, starting from now given a 6 percent rate and semi-annually compunding?

A. How much must you deposit each six months?

Answer 1

If we first calculate, how many pament per periode we have to make, we can obtain:

0                1                     2                      3                      4                     5 Years

0 1          2          3          4          5          6          7          8          9         10 Periods

So, here we can see, we have to deposit twice in a year , that is for 5 years, we need to do a total of (5*2) = 10 deposits. So, the no. of periods of compounding will be 10%

Now if we calculate the Annuity formula,i.e,

Where, FV = Future Value = 7500

r = interest rate in percent per period = 6% = 0.06

n = number of periods = 10

So, I have to deposit 569 each six months.