MATH SOLVE

3 months ago

Q:
# A loan of $46,000 is made at 7% interest, compounded annually. After how many years will the amount due reach $65,000 or more?

Accepted Solution

A:

After 5.11 years, amount due reach $65,000 or moreSolution:Given that a loan of $46,000 is made.
Rate of interest charged is 7% compounded annually
Need to determine number of years in which the amount due reach $65,000 or more.
In our case
Amount due A = $65000
Loan Amount that is principal P = $46000
Rate of interest r = 7%
Formula for Amount compounded anually is as follows:[tex]\mathrm{A}=P\left(1+\frac{r}{100}\right)^{n}[/tex]Substituting the values in above formula we get[tex]\begin{array}{l}{65000=46000\left(1+\frac{7}{100}\right)^{n}} \\\\ {\frac{65000}{46000}=\left(\frac{107}{100}\right)^{n}} \\\\ {\Rightarrow 1.4130=(1.07)^{n}}\end{array}[/tex]Applying log on both sides, we[tex]\begin{array}{l}{\ln 1.4130=n \ln 1.07} \\\\ {=>\frac{\ln 1.4130}{\ln 1.07}=\mathrm{n}} \\\\ {=>\mathrm{n}=\frac{0.34571}{0.067658}=5.1096=5.11}\end{array}[/tex]Hence after 5.11 years , amount due reach $65,000 or more