Question

A deposit of $1000 is made into an account at the beginning of each year for 30 years and earns 6% interest compounded annually. What is the value in the account at the end of thirtieth year?

I need this quick please!!!

Answer 1

I think it is about 13780 but I am not sure

Answer 2

Deposit made each year = $1000

Compound interest = 6%

Time period = 30 years

When a deposit is made each year with interest compounded annually, total amount after a certain time period is given as:

`P_N =(d((1+(r)/(k))^(Nk)-1))/((r)/(k))`

where,

`P_N` = total amount in account after N years.

d = deposit made

r = annual rate of interest in decimal form.

k = number times deposit made in one year.

`P_N =(1000((1 +(0.06)/(1))^((30*1)) -1))/((0.06)/(1))`

`P_N =(1000((1+0.06)^(30)-1))/(0.06)`

`P_N =(1000((1.06)^(30)-1))/(0.06)`

`P_N =(1000(5.743 - 1))/(0.06)`

`P_N =(1000 * 4.743)/(0.06)`

`P_N =(4743)/(0.06)`

`P_N = 79050`

Hence, value in the account at the end of 30th year = $79050