Loan Question

Question

A $4900 loan at 9.6% compounded monthly was settled by a single payment of $5900 including accrued interest. Rounded to the nearest day, how long after the initial loan was the $5900 payment made? For the purpose of determining the number of days in a partial month, assume that a full month has 30 days. (Do not round intermediate calculations.)

Answer 1

The standard equation to use is A=P(1+R/N)^(N*T) where A is the final amount, P is the Principle invested, R is the rate (as a decimal, not a percent), N is the number of times a year it is compounded and T is the time in years.

 

We substitute from the original problem:

 

5900 = 4900(1+.096/12)^(12*T), therefore we need to solve for t (in years) and then convert it to days.

 

59/49 = (1.008)^(12*T)  to solve an exponential equation, we take the log of both sides

 

Log(59/49) = Log(1.008)^12*T  the power rule allows us to move the 12*T outside the Log

 

Log (59/49) = 12*T*Log(1.008)

 

Log(59/49) / Log (1.008) = 12*T

 

Log (59/49) / Log (1.008) / 12 = T

 

T=1.9423 years

 

1.9423 years * 365 = 708.93 days, rounded up to 709 days