Question

how much must be deposited at the beginning of every six months in an account that pays 6% compounded semi-annually so that the account will contain 35,000 at the end of five years the semi-annual payments are___?round to 2 decimal places

Answer 1

In order to determine the initial investment, use the following formula for the composed interest:

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

where:

P: initial investment = ?

r: interest rate = 6% = 0.06

n: number of times per time period = 6

t: time period = 5 x 2 = 10

I: final account = 35,000

replace the previous values of the parameters and solve for P, as follow:

`\begin{gathered} 35000=P(1+0.06/6)^(6\cdot10)=P\cdot1.816 \\ P=35000/1.816 \\ P=19273.13 \end{gathered}`

Hence, the initial investment was 19,273.13