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

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A savings account is started with an initial deposit of \$500. The account earns 1.5% interest compounded annually Feb 12, 2018

### Best Answer

#1
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(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 .)

Feb 13, 2018

### 1+0 Answers

#1
+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