Question

Jennifer opted for the plan that will pay her $ 52,000 annually for 15 years. The cash will be paid at the end of each year

Required

A. Assuming that the interest will remain at 6.8 % constant over the whole period , how much will the insurance company disburse at the end of the 15 years of annuity payment to Jennifer? [ordinary annuity]

B. If the payment of the cash flow is done in the beginning of the period , what will be the sum for the insurance company will disburse? [interest rate changes to 7.5%]

C. If Jennifer is supposed to invest a sum at the beginning of the retirement in the annuity fund of the insurance , calculate the sum she has to give to the company if

a. Payment is received at the end of each period and the interest rate is 4.8%

b. Payment is done at the beginning of each period and the interest rate is 5.8%

[ Annual payment = $52,000 and period is 15 years]

Answer 1

(a)Future Value of an Annuity

ordinary annuity formula$=P\times \frac{(1+r)^{n}-1}{r}$

P = the annuity payment , r = the interest rate per time period, and n = the number of time periods.

$=52000\times \frac{(1+0.068)^{15}-1}{0.068}\\=52000\times \frac{1.6827}{0.068}\\=52000\times 24.745\\=\$1286754.911$

(b)Future Value of an Annuity

Due (FVAD) Formula$=P×\frac{(1 + r)^n - 1}{r}+P(1 + r)^n-P$

P = the annuity payment , r = the interest rate per time period, and n = the number of time periods.

$=52000×\frac{(1 + 0.075)^{15} - 1}{0.075}+52000(1 + 0.075)^{15}-52000\\= (52000\times 26.118)+(52000\times2 .959)-52000\\=1358154.965+153861.6223-52000\\=\$1460016.587$

(c)

(a))Future Value of an Annuity

ordinary annuity formula$=P\times \frac{(1+r)^{n}-1}{r}$

P = the annuity payment , r = the interest rate per time period, and n = the number of time periods.

$=52000\times \frac{(1+0.068)^{15}-1}{0.048}\\=52000\times \frac{1.0203}{0.048}\\=52000\times 21.257\\=\$1105342.013$

(b)Future Value of an Annuity

Due (FVAD) Formula$=P×\frac{(1 + r)^n - 1}{r}+P(1 + r)^n-P$

P = the annuity payment , r = the interest rate per time period, and n = the number of time periods.

$=52000×\frac{(1 + 0.058)^{15} - 1}{0.058}+52000(1 + 0.058)^{15}-52000\\= (52000\times 22.924)+(52000\times 2.33)-52000\\=1192072.964+121140.2203-52000\\=\$1261212.984$