Question

Erin currently has $44,000 in an account. She will deposit $10,000 every other year beginning next year and ending nine years from today. She will have $_____ in her account 10 years from today. Assume the account pays 5% per annum.

Answer 1

She will have $136,094.71 in her account 10 years from today
We can solve this problem by applying following two formula:
Firstly calculate the future value of an investment as follows
FVn= PV (1 + I)^n
Where,
FV = Future value at the end of year n
PV = Present value
I = Interest rate
n = number of compounding period
Given,
PV = $44,000
I = 5% p.a.
n = 10 years
FV at year 10 = $44,000 * (1 + .05)^10
FV at year 10 = $44,000 * 1.6289
FV at year 10 = $71,671.36
Secondly calculate the future value(FV) of the deposits as follows:
FV of Annuity = P * (((1 + r)^n - 1)/r)
Where,
P = Periodic Payment
r = rate per period
n = number of periods
Given,
P = $10,000
given r = 5% is for per year and periodic payment is in every 2 year
therefore rate per period can be calculated as follows:
r = (1+r)^2 - 1
r = (1+.05)^2 - 1
r = 1.1025 - 1
r = 0.1025
r = 10.25%
n = 5 (Since she will deposit $10,000 every other year which will beginning
next year and ending nine years from today, that is, she will deposit
in year 1st, 3rd, 5th, 7th, 9th)
Now,
FV of Annuity at year 9 = $10,000 * (((1 + 0.1025)^5 - 1)/0.1025)
FV of Annuity at year 9 = $10,000 * ((1.628895 - 1)/0.1025)
FV of Annuity at year 9 = $10,000 * (0.628895/0.1025)
FV of Annuity at year 9 = $10,000 * 6.135557
FV of Annuity at year 9 = $61,355.57
Now,
FV of Annuity at year 10 = FV of Annuity at year 9 * (1 + r p.a.)
FV of Annuity at year 10 = $61,355.57 * (1+.05)
FV of Annuity at year 10 = $64,423.35
Amount in her account 10 years from today = FV of investment + FV of Annuity
Amount in her account 10 years from today = $71,671.36 + $64,423.35
Amount in her account 10 years from today = $136,094.71