Alfred is saving up money for a down payment on a house. He currently has $4185, but knows he can get a loan at a lower interest rate if he can put down $5019. If he invests the $4185 in an account that earns 4.1% annually, compounded quarterly, how long will it take Alfred to accumulate the $5019? Round your answer to 2 decimal places.

Question

Alfred is saving up money for a down payment on a house.  He currently has $4185, but knows he can get a loan at a lower interest rate if he can put down $5019.  If he invests the $4185 in an account that earns 4.1% annually, compounded quarterly, how long will it take Alfred to accumulate the $5019?  Round your answer to 2 decimal places.

Henry · Accepted Answer

P = Po(1+r)^n.

Po = $4185.

r = (4.1%/4)/100% = 0.010.

n = 4Comp./yr. * t yrs. = 4t Compounding periods.

P = 4185(1.010)^4t = 5019.
1.010^4t = 1.19928.
4t*Log 1.010 = Log 1.19928.
4t = Log 1.19928/Log 1.010. 18.26.
t = 4.57 Yrs.