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# A person invests \$500 in an account that earns a nominal yearly interest rate of 4%.

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A person invests \$500 in an account that earns a nominal yearly interest rate of 4%. Someone, please solve this little by little I'm really confused! Mar 19, 2019

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a. if the interest rate is 4% , the account will grow 4% more than the year before  EACH YEAR

initial 500 deposit will be worth   500 x 1.04 at the end of year 1 = \$520

at the end of the SECOND year, due to compounding, it will be worth   520 x 1.04=\$ 540.80

after 10 years    the formula becomes    500 (1.04)^10 = \$ 740.12

b.1.04 is the interst applied PER YEAR     .... now the compounding period is 3 months....4 PERIODS per year..

..the periodic interest is then  .04/4 = .01/period    for 40 periods (10 years)

and the formula becomes

500 (1.01)^40 = 744.43      NOTE: Due to COMPOUNDING this works out to be GREATER than 4% per year

(perhaps you have heard "APR"   = annual percentage rate     or

APY = annual percentage yield)

c. 1.04  = (1+x)^4      x = .009853  or 0..09853 %  per quarter compounding

d.  500 (1+ .009853)^40 = 740.12

Mar 19, 2019
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Thanks so much! I'm glad you helped me GAMEMASTERX40  Mar 19, 2019
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You are welcome....this stuff will be very important to you later in your financial life (REALLY!)....learn it well!  ~EP

Mar 19, 2019
edited by ElectricPavlov  Mar 19, 2019