Respuesta :
Answer:
[tex]\$1762.86[/tex]
Step-by-step explanation:
GIVEN: You deposit [tex]\$1000[/tex] in an account that pays [tex]7\%[/tex] interest compounded semiannually. After [tex]4[/tex] years, the interest rate is increased to [tex]7.36%[/tex] compounded quarterly.
TO FIND: What will be the value of the account after a total of [tex]8[/tex] years.
SOLUTION:
Total initial amount deposited in account [tex]=\$1000[/tex]
rate of interest for first [tex]4\text{ years}[/tex][tex]=7\%[/tex]
As interest compounds semiannually, it compounds twice a year
Amount generated by compound interest [tex]=P(1+\frac{r}{n})^n^t[/tex]
Here initial Principal amount [tex]P=\$1000[/tex]
Here total duration [tex]nt=4\text{ years}[/tex]
total number of times compounding done [tex]n=2[/tex]
putting values
[tex]=1000(1+\frac{7}{100\times2})^4[/tex]
[tex]=\$1316.81[/tex]
after [tex]4\text{ years}[/tex] the rate is changed and the amount generated after first [tex]4\text{ years}[/tex] will be the new principal amount
new Principal amount [tex]P=\$1316.81[/tex]
total duration [tex]nt=4\text{ years}[/tex]
compounding done in a year [tex]n=4[/tex]
new rate of interest [tex]r=\$7.36\%[/tex]
putting values in above mentioned formula
[tex]=1316.81(1+\frac{7.36}{100\times4})^4[/tex]
[tex]=\$1762.86[/tex]
Hence after [tex]8[/tex] years there will be [tex]\$1762.86[/tex] in account.
