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Evgesh-ka [11]
3 years ago
9

ou wish to retire in 20 years, at which time you want to have accumulated enough money to receive an annual annuity of $32,000 f

or 25 years after retirement. During the period before retirement you can earn 8 percent annually, while after retirement you can earn 10 percent on your money. What annual contributions to the retirement fund will allow you to receive the $32,000 annuity
Business
1 answer:
AleksAgata [21]3 years ago
3 0

Answer:

Annual contributions to the retirement fund will be $6,347.31

Explanation:

First find the Present Value of the Annuity giving payments of $32,000 annually for 25 years at the rate of 10%.

Using a Financial Calculator enter the following data

PMT = $32,000

P/y = 1

N = 25

R =  10%

FV = 0

Thus, the Present Value, PV is $290,465.28

At the time of retirement (in 20 years time) the Value of the annuity fund is $290,465.28.

Next we need to find the Payments PMT to reach this amount in 20 years time at the interest rate of 8%

Using a Financial Calculator enter the following data

FV = $290,465.28

N = 20

R = 8 %

PV = $0

Thus, the Payments, PMT required will be $6,347.3080

Conclusion :

Annual contributions to the retirement fund will be $6,347.31

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3 years ago
At the end of every 3 months, Teresa deposits into an account that pays 5% compounded quarterly. After she puts the accumulated
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Answer:

The amount Teresa will have accumulated when this certificate matures is $2,452.16.

Explanation:

Note: This question is not complete as some important data are omitted. The complete question is therefore provided before answering the question as follows:

At the end of every 3 months, Rita deposits $100 into an account that pays 5% compounded quarterly. After 5 years, she puts the accumulated amount into a certificate of deposit paying 8.5% compounded semiannually for 1 year. When this certificate matures, how much will Teresa have accumulated?

The explanation of the answers is now provided as follows:

Step 1: Calculation of accumulated amount after 5 years.

Since the deposits are paid at the end of every 3 months, the accumulated amount after 5 years can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:

FV5 = P * (((1 + r1)^n1 - 1) / r) ................................. (1)

Where,

FV5 = Future value or accumulated amount after 5 years = ?

P = Quarterly deposit or deposit at the end of every 3 months = $100

r = Quarterly interest rate on the account = Interest rate on the account / Number of quarters in a year = 5% / 4 = 0.05 / 4 = 0.0125

n = number of quarters = 5 years * Number of quarters in a year = 5 * 4 = 20

Substituting the values into equation (1), we have:

FV5 = $100 * (((1 + 0.0125)^20 - 1) / 0.0125) =  $2,256.30

Therefore, the accumulated amount after 5 years is $2,256.30.

Step 2: Calculation of the amount Teresa will have accumulated when this certificate matures.

This can be calculated using the simple future value (FV) as follows:

FVM = FV5 * (1 + R)^N ……………………… (2)

FVM = Accumulated amount at maturity = ?

R = semi-annual interest rate on certificate of deposit = Interest rate on certificate of deposit / Number of semiannuals in a year = 8.5% /2 = 0.085 / 2 = 0.0425

N = number of semiannuals = 1 year * Number of semiannuals in a year = 1* 2 = 2

Substituting the values into equation (2), we have:

FVM = $2,256.30 * (1 + 0.0425)^2 = $2,452.16

Therefore, the amount Teresa will have accumulated when this certificate matures is $2,452.16.

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Answer:

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