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

Today is Sept. 1, 2009. Starting today you plan to invest $1000 every year, first deposit today and last deposit on Sept. 1, 2025. After that, you plan to leave the money in the same account until Sept. 1, 2030. However, the interest rate is 8% compounded quarterly until your last deposit and only 7% compounded annually after 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

Solutions

Expert Solution

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

jeff jeffy answered 1 year ago
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