Today is Sept. 1, 2009. Starting today you plan to invest $1000 every year, first deposit...

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Today is Sept. 1, 2009. Starting today you plan to invest $1000every year, first deposit today and last deposit on Sept. 1, 2025.After that, you plan to leave the money in the same account untilSept. 1, 2030. However, the interest rate is 8% compoundedquarterly until your last deposit and only 7% compounded annuallyafter that. How much money will you have in your account on Sept.1, 2030?
a. $34,504.14
b. $35,504.14
c. $48,393.84
d. $49,005.74
e. None of the above

Answer & Explanation Solved by verified expert

4.1 Ratings (658 Votes)

Since rate of interest given is compounded quarterly, we have to convert the rate
to effective rate annually using (1+r/n)^n-1
Here r = 8%, n = 4
(1+.02)^4-1
8.2432%		so effective rate is 8.2432

From Sep 1, 2009 to Sep 1, 2025, there is 17 years of deposit

Using Future value of annuity formula

FVA = A x[ (1+r)^t-1]/r
Here, A = 1000
r = 8.243216%
t = 17

FVA = 1000 x[ (1+8.243216%)^17-1]/8.243216%
FVA = 1000 x 34.50414
FVA = 34,504.14

Now this value is further invested for 5 years

FV = P(1+r)^t
Here P = 34504.14
r = 7%
t = 5

FV = 34504.14(1+.07)^5
FV = 48,393.84		Option C is correct

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Transcribed Image Text

Today is Sept. 1, 2009. Starting today you plan to invest $1000every year, first deposit today and last deposit on Sept. 1, 2025.After that, you plan to leave the money in the same account untilSept. 1, 2030. However, the interest rate is 8% compoundedquarterly until your last deposit and only 7% compounded annuallyafter that. How much money will you have in your account on Sept.1, 2030?a. $34,504.14b. $35,504.14c. $48,393.84d. $49,005.74e. None of the above