Question

3. A saver wants $100,000 after ten years and believes that it is possible to earn an annual rate of 8 percent on invested funds.

What amount must be invested each year to accumulate $100,000 if (1) the payments are made at the beginning of each year or (2) they are made at the end of each year?

How much must be invested annually if the expected yield is only 5 percent?

please explain step by step process.DO NOT COPY AND PASTE PREVIOUS ANSWERS

Answer 1

1

Payments made at the beginning of the year

Future value of annuity,

FV of annuity = P*[((1+r)^n - 1)/r] * (1+r)
P - Periodic payment = ?
r - rate per period = 0.08
n - number of periods = 10

100000 = P*(((1+0.08)^10 - 1)/0.08) * (1+0.08)

P = $6391.62

2.

If the payments are made at the end of year

FV of annuity = P*[((1+r)^n - 1)/r]
P - Periodic payment = ?
r - rate per period = 0.08
n - number of periods = 10

100000 = P*(((1+0.08)^10 - 1)/0.08)

P = $6902.95

B.

If yield is 5%

Payments made at the beginning of the year

Future value of annuity,

FV of annuity = P*[((1+r)^n - 1)/r] * (1+r)
P - Periodic payment = ?
r - rate per period = 0.05
n - number of periods = 10

100000 = P*(((1+0.05)^10 - 1)/0.05) * (1+0.05)

P = $7571.86

2.

If the payments are made at the end of year

FV of annuity = P*[((1+r)^n - 1)/r]
P - Periodic payment = ?
r - rate per period = 0.05
n - number of periods = 10

100000 = P*(((1+0.05)^10 - 1)/0.05)

P = $7950.46