Answer:
A) $9458.51
B) 5.09% (2 d.p.)
Step-by-step explanation:
Part A
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
- A = final amount
- P = principal amount
- r = interest rate (in decimal form)
- n = number of times interest applied per time period
- t = number of time periods elapsed
Given:
- P = $9000
- r = 5% = 0.05
- n = 4 (quarterly)
- t = 1 year
Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=9000\left(1+\frac{0.05}{4}\right)^{4 \times 1}[/tex]
[tex]\implies \sf A=9000(1.0125)^4[/tex]
[tex]\implies \sf A=9458.508032...[/tex]
Therefore, the value of the account after 1 year is $9458.51.
Part B
Simple Interest Formula
A = P(1 + rt)
where:
- A = final amount
- P = principal
- r = interest rate (in decimal form)
- t = time (in years)
Given:
- A = $9458.51
- P = $9000
- t = 1 year
Substitute the given values into the formula and solve for r:
[tex]\implies \sf 9458.51=9000(1+r(1))[/tex]
[tex]\implies \sf 9458.51=9000(1+r)[/tex]
[tex]\implies \sf \dfrac{9458.51}{9000}=1+r[/tex]
[tex]\implies \sf r=\dfrac{9458.51}{9000}-1[/tex]
[tex]\implies \sf r=0.050945...[/tex]
[tex]\implies \sf r=5.0945... \%[/tex]
Therefore, the effective annual yield is 5.09% (2 d.p.).
