Question

Gerry plans to make four annual deposits of $4000 into an account that pays 5.2%. The first deposit will occur in 2020. What size equal annual withdrawals can Gerry make from the account if the first withdrawal occurs in 2026 and the last occurs in 2031

Answer 1

Answer:

PMT = $3794.46

Explanation:

given data

rate = 5.2 %

annual deposits = $4000

time = 4

solution

we apply here future value formula that is

future value = PMT ×   $\frac{(1+r)^t-1 }{r}$     .....................1

put here value

future value = 4000 × \frac{(1+0.052)^{4}-1 }{0.052}  

future value = $17291.83  

and

future value for next 2 year

future value = 17291.83   × ${(1+0.052)^{2} }$  

future value = $19136.93  

and

present value of 6 year PMT will be

present value  = PMT × $\frac{1 - (\frac{1}{(1+r)^t}}{r}$

PMT =present value ×  $\frac{r}{1 - (\frac{1}{(1+r)^t})}$

PMT = 19136.93   ×  $\frac{0.052}{1 - (\frac{1}{(1+0.052)^6})}$

PMT = $3794.46