can you solve this correctly please thank you An initial dep

can you solve this correctly please thank you

An initial deposit of $5000 is put into an account that earns 4% interest, compounded annually. Each year, an additional deposit of $5000 is added to the account What is the value of the account after the tenth deposit if no withdrawals or additional deposits are made?

Solution

The formula for calculating the future value of an annuity due, where a series of equal payments are made at the beginning of each of multiple consecutive periods, is F = P (1 + r)[{(1 + r)ⁿ – 1} / r]. Here, P is the periodic payment, r is the rate of interest in decimals, and n is the number of periods. In this case, P = $ 5000, n = 10 and r = 0.04. Then F = 5000(1+0.04)[ {(1+0.04)¹⁰ -1}/0.04] = 5000(1.04)[(1.04)¹⁰ -1]/0.04 = (5200/0.04)* (1.480244285 -1) = 130000*0. 480244285 = $ 62717.57 (on rounding off to the nearest cent)