Question

I now have $16,000 in the bank earning interest of 1.00% per month. I need $26,000 to make a down payment on a house. I can save an additional $100 per month. How long will it take me to accumulate the $26,000? (Do not round intermediate calculations. Round your answer to 2 decimal places. Use a financial calculator or Excel.)

Answer 1

time = 32.70

Step-by-step explanation:

given data

present value = $16000

earning interest = 1.00% per month

future value = $26,000

save additional = $100 per month

solution

we apply here future value annuity formula that is

future value annuity = present value ×
`(1+r)^(t)` + payment ×
`((1+r)^t-1)/(r)` ..........1

put here value and we get

$26,000 = $16000 ×
`(1+0.01)^(t)` + $100 ×
`((1+0.01)^t-1)/(0.01)`

$26000 = $16000 ×
`1.01^t` - 1 + $1000 × (
`1.01^t-1` )

$36000 + 1 = $26000 ×
`1.01^t`

take ln both side and solve

t = 32.70