Mathematics, 15.04.2020 01:37 aaron0828

An initial investment of $1000 is deposited in an account with a 1.2%
interest rate, compounded annually. In how many years will the
account reach $1500?

Answers: 1

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Answers

34 years will the account reach $1500, if An initial investment of $1000 is deposited in an account with a 1.2% interest rate, compounded annually.

Step-by-step explanation:

The given is,

Initial investment of $1000

Interest rate 1.2%, compounded annually

Future amount $1500

Step:1

Formula to calculate the future amount with an interest rate of compounded annually,

$F=P(1+\frac{r}{n} )^{nt}$ ............................(1)

Where,

F - Future worth amount

P - Initial investment

r - Rate of interest

n - No.of compounding in a year

t - No.of years

From given,

F = $1500

P = $1000

r = 1.2%

n = 1 (compounded annually)

Equation (1) becomes,

$1500=1000(1+\frac{0.012}{1} )^{(1)(t)}$

$\frac{1500}{1000} =(1+\frac{0.012}{1} )^{(t)}$

$1.5 =(1+\frac{0.012}{1} )^{(t)}$

$1.5 =(1+0.012 )^{(t)}$

$1.5 =(1.012 )^{(t)}$

Take log on both sides,

log 1.5 = {(t)} log (1.012 )

Substitutes log values,

0.17609126 =( t ) 0.0051805

$t = \frac{0.17609126}{0.0051805}$

t = 33.99

t ≅ 34 years

Result:

34 years will the account reach $1500, if An initial investment of $1000 is deposited in an account with a 1.2% interest rate, compounded annually.

Answer from: Quest

you probably already have the answer but anyways it's b. 15.0

step-by-step explanation:

Answer from: Quest

fwms@lil_ben06

step-by-step explanation:

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