Question

Alexandra plans to deposit $1,000 into a fund at the end of each of the next eight years. If her fund earns 4.75 percent compounded annually, how much will she have at the end of eight years?
A. $8,340
B. $8,525
C. $8,856
D. $9,297
E. $9,464

Randolph will receive a 20-year annuity with annual payments of $150. The first payment will be received at the end of Year 1, and the last payment will be received at the end of Year 20. Randolph will invest each payment in an account that pays 8.25 percent. What will be the value in his account at the end of Year 30?
A. $16,631
B. $15,593
C. $14,175
D. $13,340
E. $18,034

Boris makes monthly payments of $175 into a fund at the end of each month for the next eight years. The
fund pays an annual interest rate of 7.5 percent (compounded monthly). If he continues to hold the money in
the account for an additional four years, what will be the value in his account at the end of Year 12?
A. $22,924
B. $29,427
C. $30,598
D. $30,915
E. $40,676

Answer 1

Question 1st:

This is the question of future value of an annuity.

Future value of annuity = Annuity amount*FV factor of annuity

FV Factor of annuity=[(1+r)^ⁿ-1]/r

=[(1+.0475)^{^8}-1]/.0475

=.44955/.0475

=9.4642

Future value of annuity = 1000*9.4642

=9464.2

Hence answer is (e) 9464.

Q2nd:

Future value of annuity = Annuity amount*FV factor of annuity

FV Factor of annuity=[(1+r)^ⁿ-1]/r

=[(1+.0825)^{^20}-1]/.0825

=3.881554/.0825

=47.04914

Future value of annuity = 150*47.04914

=7057.37

Future value of $7057.37 after next 10 years shall be: [(1.0825)^10]*7057.37

=15592.72 or 15593

Hence answer is (B) 15593

Q:3

As the interest rate is 7.5% (Compounded monthly)

Monthly rate shall be=7.5/12

=.625% or .00625

Number of periods shall be=96(i.e.8*12)

Future value of annuity = Annuity amount*FV factor of annuity

FV Factor of annuity=[(1+r)^ⁿ-1]/r

=[(1+.00625)^{^96}-1]/.00625

=.81872/.00625

=130.9951

Future value of annuity = 175*130.9951

=22924.15

Future value of $22924.15 after next 4 years shall be: [(1.00625)^⁴⁸]*22924.15

=30915.49 or 30914

Hence answer is (D) 30914

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