Pedro deposits dollar sign, 700$700 every month into an account earning a monthly interest rate of 0.4%. How many years would it be until Pedro had dollar sign, 28, comma, 000$28,000 in the account, to the nearest tenth of a year? Use the following formula to determine your answer.
A, equals, d, left bracket, start fraction, left bracket, 1, plus, i, right bracket, to the power n , minus, 1, divided by, i, end fraction, right bracket
A=d(
i
(1+i)
n
−1
)
A, equalsA= the future value of the account after n periods
d, equalsd= the amount invested at the end of each period
i, equalsi= the interest rate per period
n, equalsn= the number of periods
A, equals, d, left bracket, start fraction, left bracket, 1, plus, i, right bracket, to the power n , minus, 1, divided by, i, end fraction, right bracket
A=d(
i
(1+i)
n
−1
)
A, equalsA= the future value of the account after n periods
d, equalsd= the amount invested at the end of each period
i, equalsi= the interest rate per period
n, equalsn= the number of periods
d, equals, 700, left bracket number of dollars per month right bracket
d=700 (number of dollars per month)
A, equals, 28000, left bracket future account value right bracket
A=28000 (future account value)
i, equals, 0, point, 0, 0, 4, left bracket interest rate per month right bracket
i=0.004 (interest rate per month)
Plug everything in:
Plug everything in:
28000, equals, 700, left bracket, start fraction, left bracket, 1, plus, 0, point, 0, 0, 4, right bracket, to the power n , minus, 1, divided by, 0, point, 0, 0, 4, end fraction, right bracket
28000=700(
0.004
(1+0.004)
n
−1
)
28000, equals, 700, left bracket, start fraction, 1, point, 0, 04, to the power n , minus, 1, divided by, 0, point, 0, 0, 4, end fraction, right bracket
28000=700(
0.004
1.004
n
−1
)
start fraction, 28000, divided by, 700, end fraction, equals, start fraction, 700, left bracket, start fraction, 1, point, 0, 04, to the power n , minus, 1, divided by, 0, point, 0, 0, 4, end fraction, right bracket, divided by, 700, end fraction
700
28000
=
700
700(
0.004
1.004
n
−1
)
40, equals, start fraction, 1, point, 0, 04, to the power n , minus, 1, divided by, 0, point, 0, 0, 4, end fraction
40=
0.004
1.004
n
−1
0, point, 0, 0, 4, left bracket, 40, right bracket, equals, left bracket, start fraction, 1, point, 0, 04, to the power n , minus, 1, divided by, 0, point, 0, 0, 4, end fraction, right bracket, left bracket, 0, point, 0, 0, 4, right bracket
0.004(40)=
(
0.004
1.004
n
−1
)(0.004)
0, point, 1, 6, equals, 1, point, 0, 04, to the power n , minus, 1
0.16=
1.004
n
−1
plus, 1, plus, 1
+1=
1.004
n
+1
1, point, 1, 6, equals, 1, point, 0, 04, to the power n
1.16=
1.004
n
log, left bracket, 1, point, 1, 6, right bracket, equals, log, left bracket, 1, point, 0, 04, to the power n , right bracket
log(1.16)=
log(1.004
n
)
log, left bracket, 1, point, 1, 6, right bracket, equals, n, log, left bracket, 1, point, 0, 0, 4, right bracket
log(1.16)=
nlog(1.004)
start fraction, log, left bracket, 1, point, 1, 6, right bracket, divided by, log, left bracket, 1, point, 0, 0, 4, right bracket, end fraction, equals, start fraction, n, log, left bracket, 1, point, 0, 0, 4, right bracket, divided by, log, left bracket, 1, point, 0, 0, 4, right bracket, end fraction
log(1.004)
log(1.16)
=
log(1.004)
nlog(1.004)
37, point, 1, 7, 9, 1, 6, 1, 9, 1, equals, n
37.17916191=
n
n, equals, 37, point, 1, 7, 9, 1, 6, 1, 9, 1, months
n=37.17916191 months
Convert months to years:
Convert months to years:
37, point, 1, 7, 9, 1, 6, 1, 9, 1, divided by, 12
37.17916191÷12
3, point, 0, 9, 8, 2, 6, 3, 4, 9
3.09826349