A man makes $10 deposits each quarter into a savings account earning 8% interest

Question

A man makes $10 deposits each quarter into a savings account earning 8% interest compounded quarterly. He continues these deposits for 12 years. How much will the account be worth after 12 years? A credit card bill shows a balance due of $750 with a minimum payment of $15 and a monthly interest rate of 1.62%. What is the EAR? Find the future value of an annuity with monthly deposits of $250, made over a period of eight years, with 6% interest compounded monthly. How much would be have to invest each month in an annuity earning 5% monthly to earn $30,000 at the end of 30 years? Which of these savings rates is most favorable/

Explanation / Answer

(10) (A)

Quarterly interest = 8% / 4 = 2%

Number of quarters = 12 x 4 = 48

FV = Annuity x Future Value Interest Factor of Annuity (2%, 48 periods)

= $10 x 79.3535 (From FVIFA table)

= $793.54

(11) (D)

EAR = (1.0162)12 - 1 = 1.2126 - 1 = 0.2126 or 21.26%

(12) (D)

Monthly interest = 6% / 12 = 0.5%

Number of months = 12 x 8 = 96

FV = Annuity x Future Value Interest Factor of Annuity (0.5%, 96 periods)

= $250 x 122.8285 (From FVIFA table)

= $30,707

(13) (B)

Monthly interest = 5% / 12 = 0.42%

Number of months = 12 x 30 = 360

Annuity = FV / FVIFA (0.42%, 360 periods)

= $30,000 / 838.4415 (From FVIFA table)

= $35.8

NOTE: The slight difference in answer is due to rounding off of FVIFA factor.

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