Respuesta :
We have:
No. of payments n = 10x 4 = 40
Periodic payment pmt = $7000
Period rate r= 12%/4 = 3%
We can use the following formula to calculate the Future value:
[tex] FV=pmt \frac{(1+r)^{n}-1}{r} [/tex]
plugging the values in the formula, we get:
[tex] FV=7000 \frac{(1+0.03)^{40}-1}{0.03} = 7000 \times 75.40126 =$527808.82 [/tex]
Answer : The calculated answer of FVA is $ 2,57,499.14. This is closest to $257,502.00 - option B.
We follow these steps to arrive at the answer:
We use the Future Value of Annuity formula to arrive at the answer to this question, as the new account begins at $0.00 and there is no mention of the amount in the previous account.
The formula for Future Value of annuity is:
[tex] FVA =P * \frac{\left (1+r\right )^n - 1}{r} [/tex]
where
P = constant periodic contribution
r = rate per period
n = number of periods.
In the question above, P = $7,000.
The given interest rate is 12% p.a. Since the contributions are made semi-annually (twice a year), we need to find the rate per period with the following formula:
[tex] \ r = \frac{Interest rate per year}{No. of compounding periods per yr} [/tex]
So, we get
r = [tex] \ r = \frac{0.12}{2} [/tex]
r = 0.06
Since there are two compounding periods per year, we get number of compounding periods 'n', by
[tex] \ n = No. of years * No. of compounding periods [/tex]
So, [tex] n = 10 * 2 [/tex]
n = 20
Substituting the values of P, n and r in the FVA equation we get,
[tex] FVA =3,500 * \frac{1.06^{20}- 1}{0.06} [/tex]
[tex] FVA =3,500 * \frac{2.207135472}{0.06} [/tex]
[tex] FVA =3,500 * 36.7855912 [/tex]
[tex] FVA = $ 2,57,499.14 [/tex]
