Question

A person invest 1500 dollars in a bank. The bank pays 6.25% interest compounded daily. To the neatest tenth of a year, how long must the person leave the money in the bank until it reaches 4000 dollars?​

Answer 1

Answer:

15.6 years

Step-by-step explanation:

We calculate the effective annual rate for 6.25% compounded daily:

$i_n=(1+i/n)^n-1 \ \ \, n=365, i=6.25\%\\\\i_{365}=(1+0.0625/365)^{365}-1\\\\i_{365}=0.064488763$

Given the principal amount as $1500 and the future value as $4000, the number years is calculated as:

$FV=P(1+i)^n, \ \ \ \ \ P=1500, FV=4000, i=0.064488763\\\\4000=1500(1+.064488763)^n\\\\\frac{8}{3}=1.064488763^n\\\\n=\frac{log(\frac{8}{3})}{log \ 1.064488763}\\\\n=15.6$

Hence, the term of the loan is 15.6 years