Question

A certain savings and loan company advertises that is pays 6% nominal interest, compounded quarterly. What is the effective interest rate per annum? If you deposit $6000 now and plan to withdraw it in five years, how much would the account be worth at that time?  (Hint: to find the effective interest rate, use the formula: (1 + r/M)^M-1.)

Answer 1

Normal rate (r) = 6%

Compounding = Quarterly

Compounding in a year (m) = 4

Effective interest rate per annum = [(1 + r/m)^{m -} 1]

= [(1 + 0.06/4)⁴ - 1]

= [(1 + 0.015)⁴ - 1]

= (1.015)⁴ - 1

= 1.0614 - 1

= 0.0614

= 6.14 (Rounded to two decimal)

Deposit = $6,000

Time period = 5 Year

Time period in Quarters (n) = 5 x 4

= 20

Interest rate = 6% annual

Quarterly interest rate (i) = 6/4

= 1.5%

Amount after 5 year = Deposit x (1 + i)ⁿ

= 6,000 x (1 + 0.015)²⁰

= 6,000 x (1.015)²⁰

= 6,000 x 1.346855

= $8,081 (Rounded to nearest whole dollar)

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