Compound interest

[Turpentine]

1. A man, who started work in 1990, planned an investment for his retirement in 2030 in the following way. On the first day of each year, from 1990 to 2029 inclusive, he is to place $100 in an investment account. The account pays 10% compound interest per annum, and interest is added on 31 December of each year of the investment.
Calculate the value of his investment on 1 January 2030.

Is there a formula for this? I tried using the geometric sum formula, but it didn't give me the correct answer.
The correct answer is $45 259.26

Thanks!

 

[Deleted member 4993]

1. A man, who started work in 1990, planned an investment for his retirement in 2030 in the following way. On the first day of each year, from 1990 to 2029 inclusive, he is to place $100 in an investment account. The account pays 10% compound interest per annum, and interest is added on 31 December of each year of the investment.
Calculate the value of his investment on 1 January 2030.

Is there a formula for this? I tried using the geometric sum formula, but it didn't give me the correct answer.
The correct answer is $45 259.26

Thanks!

What is the number of years that the money is accrued = ??

Please show your work, indicating exactly where you are stuck so that we may know where to begin to help you.

 

[TchrWill]

A man, who started work in 1990, planned an investment for his retirement in 2030 in the following way. On the first day of each year, from 1990 to 2029 inclusive, he is to place $100 in an investment account. The account pays 10% compound interest per annum, and interest is added on 31 December of each year of the investment.
Calculate the value of his investment on 1 January 2030.

Is there a formula for this? I tried using the geometric sum formula, but it didn't give me the correct answer.
The correct answer is $45 259.26

Thanks!

When an annuity is computed on the basis of the payments being made at the beginning of each period, an annuity due, the total accumulation is based on one more period minus the last payment. Thus, the total accumulation becomes

.....................S(n+1) = R[(1 + i)^(n+1) - 1]/i - R

For R = $100/month, i = .10 and n = 41 (Jan.1, 1990--> Dec. 31, 2029), the accumulation would be $48,685.18.

If the payments were made at the end of each year, an ordinary annuity, where S(n) = R[(1+i)^n - 1]/i, the accumulation would be $44,259.26.

Might your $45,259.26 be merely a typo using the ordinary annuity formula?

If payments are to be made at the beginning of each year, $48,685.18 would be the right answer.