Respuesta :
Answer:
[tex]\$65415[/tex]
Step-by-step explanation:
GIVEN: A man deposits [tex]\$16000[/tex] at the beginning of each year for [tex]16[/tex] years in an account paying [tex]5\%[/tex] compounded annually. He then puts the total amount on deposit in another account paying [tex]8\%[/tex] compounded semiannually for another [tex]8[/tex] years.
TO FIND: Find the final amount on deposit after the entire [tex]24[/tex]-year period.
SOLUTION:
Total amount deposited by man [tex]=\$16,000[/tex]
rate of interest for first 16 years [tex]=16\%[/tex]
compounding interval [tex]=1\text{year}[/tex]
Total amount after [tex]16[/tex] years [tex]=Principal(1+\frac{r}{n})^t[/tex]
[tex]=16000(1+\frac{5}{100\times1})^{16}[/tex]
[tex]=\$34,926[/tex]
this will become new principal after [tex]16[/tex] years.
rate of interest for last [tex]8[/tex] years [tex]=8\%[/tex]
compounding interval [tex]=2\text{ times}[/tex]
Total amount after [tex]24[/tex] years [tex]=34926(1+\frac{8}{100\times2})^{8}[/tex]
[tex]=\$65415[/tex]
final amount on deposit after the entire [tex]24[/tex]-year period is [tex]\$65415[/tex]
