+0

# You deposit $100 at the end of each quarter in a sinking fund earning 4% compounded quarterly. How many quarterly deposits must you make in 0 470 1 You deposit$100 at the end of each quarter in a sinking fund earning 4% compounded quarterly. How many quarterly deposits must you make in order to reach your goal of saving \$10,000? Round your answer off to the nearest whole number.

Sep 16, 2014

#1
+101741
+5

This is the furure value of an ordinary annuity problem

$$\\S=R\left[\frac{(1+i)^n-1}{i}\right]\\\\ R=100\;\;i=0.04/4=0.01\;\;S=10000,\;\;n=? \;quarters\\\\\\ 10000=100\left[\frac{(1.01)^n-1}{0.01}\right]\\\\ 1=(1.01)^n-1\\\\ 2=(1.01)^n\\\\ log2=log(1.01)^n\\\\ log2=nlog(1.01)\\\\ n=\frac{log2}{log1.01}\\\\$$

$${\frac{{log}_{10}\left({\mathtt{2}}\right)}{{log}_{10}\left({\mathtt{1.01}}\right)}} = {\mathtt{69.660\: \!716\: \!893\: \!574\: \!830\: \!3}}$$

It will take 70

70/4=17.5 years

Sep 16, 2014

#1
+101741
+5

This is the furure value of an ordinary annuity problem

$$\\S=R\left[\frac{(1+i)^n-1}{i}\right]\\\\ R=100\;\;i=0.04/4=0.01\;\;S=10000,\;\;n=? \;quarters\\\\\\ 10000=100\left[\frac{(1.01)^n-1}{0.01}\right]\\\\ 1=(1.01)^n-1\\\\ 2=(1.01)^n\\\\ log2=log(1.01)^n\\\\ log2=nlog(1.01)\\\\ n=\frac{log2}{log1.01}\\\\$$

$${\frac{{log}_{10}\left({\mathtt{2}}\right)}{{log}_{10}\left({\mathtt{1.01}}\right)}} = {\mathtt{69.660\: \!716\: \!893\: \!574\: \!830\: \!3}}$$

It will take 70

70/4=17.5 years

Melody Sep 16, 2014