series application q (1 Viewer)

[fannymasta]

at 1 july 1985, anna invested $10 000 in a bank account that paid interest at a fixed rate of 8% per annum, compounded annually.

Anna added $1000 to her account on 1 july each year, beginning on 1 july 1986. How much was in her account on 1 july 1995 after payment of interest and her deposit?

can someone please help me with this q. i keep getting it wrong

the answer is 36075.81

 

[Timothy.Siu]

at 1 july 1985, anna invested $10 000 in a bank account that paid interest at a fixed rate of 8% per annum, compounded annually.

Anna added $1000 to her account on 1 july each year, beginning on 1 july 1986. How much was in her account on 1 july 1995 after payment of interest and her deposit?

so first year, anna didn't add anything so..
just before 1 july 1986, she had $10000x1.08
before 1 july 1987 she had (10000x1.08+1000)x1.08=10000x1.08^2+1000x1.08
i shud let P=10000 R=1.08 and Q=1000
just before 1 july 1988 she had (PR^2+QR+Q)R=PR^3+QR^2+QR
so we can see a pattern sorta.
lets say 1986 is the first year,

S¹⁰=PR^10+QR^9+QR^8+...+QR
geometric sum...PR^10+QR(R^9-1)/(R-1)
=35075.81

but she also pays 1000 on that day
so $36075.81

 

[fannymasta]

at 1 july 1985, anna invested $10 000 in a bank account that paid interest at a fixed rate of 8% per annum, compounded annually.

Anna added $1000 to her account on 1 july each year, beginning on 1 july 1986. How much was in her account on 1 july 1995 after payment of interest and her deposit?

So first year, anna didn't add anything so..
Just before 1 july 1986, she had $10000x1.08
before 1 july 1987 she had (10000x1.08+1000)x1.08=10000x1.08^2+1000x1.08
i shud let p=10000 r=1.08 and q=1000
just before 1 july 1988 she had (pr^2+qr+q)r=pr^3+qr^2+qr
so we can see a pattern sorta.
Lets say 1986 is the first year,

s¹⁰=pr^10+qr^9+qr^8+...+qr
geometric sum...pr^10+qr(r^9-1)/(r-1)
=35075.81

but she also pays 1000 on that day
so $36075.81

thanks !