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A savings account is started with an initial deposit of $500. The account earns 1.5% interest compounded annually

AngelRay  Feb 12, 2018

Best Answer 

 #1
avatar+6365 
+1

(a)

 

the amount of money after  0  years   =   500

 

the amount of money after  1  year     =   500  *  1.015

 

the amount of money after  2  years   =   500 * 1.015 * 1.015

 

the amount of money after  t  years   =   500 * 1.015t

 

f(t)   =   500 * 1.015t

 

(b)

 

We want to find the value of  t  when  f(t) = 800

 

800   =   500 * 1.015t

 

1.6  =   1.015t

 

log( 1.6 )  =   log( 1.015t )

 

log( 1.6 )   =   t log( 1.015 )

 

log( 1.6 ) / log( 1.015 )   =   t

 

31.568   ≈   t

 

Since interest is added annualy, it would take  32  years for the account to have  $800 .

 

( After  31  years, it  has  $793.26  .  After 32 years, it has  $805.16 .)

hectictar  Feb 13, 2018
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1+0 Answers

 #1
avatar+6365 
+1
Best Answer

(a)

 

the amount of money after  0  years   =   500

 

the amount of money after  1  year     =   500  *  1.015

 

the amount of money after  2  years   =   500 * 1.015 * 1.015

 

the amount of money after  t  years   =   500 * 1.015t

 

f(t)   =   500 * 1.015t

 

(b)

 

We want to find the value of  t  when  f(t) = 800

 

800   =   500 * 1.015t

 

1.6  =   1.015t

 

log( 1.6 )  =   log( 1.015t )

 

log( 1.6 )   =   t log( 1.015 )

 

log( 1.6 ) / log( 1.015 )   =   t

 

31.568   ≈   t

 

Since interest is added annualy, it would take  32  years for the account to have  $800 .

 

( After  31  years, it  has  $793.26  .  After 32 years, it has  $805.16 .)

hectictar  Feb 13, 2018

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