Question

Lila and Ben are newlyweds and are hashing out their finances. They decided to deposit $5,500 annually in a joint investment account for the first 10 years of their marriage so that they can use it as a secondary retirement account. The first payment was made at the end of 2000. If the annual interest rate is 4%, how much accumulated wealth will they have at the end of the year 2025, 25 years after the first payment? Express your answer in terms of dollars, rounded to the nearest dollar.

Answer 1

first payment is made at the end of year 2000 1t_means that loth payment (final payment) _will be made at the end of year 200.9. Future value of annuity, FV 3 A (1+1) - 1 A annur -peran where, A : Amount of periodic payments it._$_5,500 no number of payments ie 10 i Interest rate per period il, 42_per_annum 10 5,500 (14100) - 1 Therefore, fv of annuity at the end of year 2009 100 1 9,500 (1.09 [1.0" 5,500 0.04 ( 1: 4802 - 1] 137,500 (0.4802) $ 66,027-50 Now, this amount [ie. $ 66,027-50) is accumulated_till 2009 end. However, the amount stays in the account_fill_the_end of 2025. Therefore, 2025- 2009 2 . 16 years

2025 Therefore the amount accumulated till the end of year FV - PV (1+i) T7 66,027.5 (1-04) : 66,027.5 [1:8730) $123,669-5 $123,670_(rounded off to nearest dollar) - I hope I've solved to the point. Please feel free to ask any queries and do give a thumbsup if the solution was satisfactory. Thank you