Question

how much must be deposited at the beginning of every six months in account that pays 6% compounded semi-annually so that account will contain 21,000 at the end of three years

Answer 1

The formula for Final Amount, A after compounding for n period of times is given by

`A=p(1+(r)/(100))^n`

Where A = amount

p= principal

r = rate (in %)

n = number of compounding periods

From the question.

A=21,000, p = ?, r=6, n = 3 x 2 = 6

`\begin{gathered} 21000=p(1+(6)/(100))6 \\ \\ 21000=p(1+0.06)^6 \\ 21000=p(1.06)6 \\ 21000=p(1.41852) \\ 21000=1.41852p \\ p=(21000)/(1.41852) \\ p=14,804.17 \end{gathered}`

The amount that must be deposited at the beginning is 14,804.17