Question

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?

Answer 1

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.

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+(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+(0.012)/(1) )^((1)(t))`

`(1500)/(1000) =(1+(0.012)/(1) )^((t))`

`1.5 =(1+(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 = (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.