Alfred is saving up money for a down payment on a townhouse

Alfred is saving up money for a down payment on a townhouse. He currently has $5016, but knows he can get a loan at a lower interest rate if he can put down $5994. If he invests the $5016in an account that earns 4.4%annually, compounded monthly, how long will it take Alfred to accumulate the $5994? Round your answer to two decimal places, if necessary.

Solution

Amount = P(1+r/n)^nt

P= $5016 , r = 4.4% = 0.044 , n=12 (compounded monthly)

For Amount= $5994

So , 5994 = 5016 (1+0.044/12)^12t

1.195 = 1.0003^12t

Taking logarithm ,

t = ln(1.195)/(12.ln(1.003)) = 4.955

t = 4.96 years