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Consider the case of the following annuities, and the need to compute either their expected rate of return or duration.
1. Matthew needed money for some unexpected expenses, so he borrowed $2,587.09 from a friend and agreed to repay the loan in three equal installments of $950 at the end of each year. The agreement is offering an implied interest rate of ___.
2. Matthew’s friend, Gregory, has hired a financial planner for advice on retirement. Considering Gregory’s current expenses and expected future lifestyle changes, the financial planner has stated that once Gregory crosses a threshold of $920,925 in savings, he will have enough money for retirement. Gregory has nothing saved for his retirement yet, so he plans to start depositing $40,000 in a retirement fund at a fixed rate of 5.00% at the end of each year. It will take ____ for Gregory to reach his retirement goal.

Respuesta :

Answer:

1. 5.00%

2. 15.70 year

Explanation:

As per the data given in the question,

1)  For computing the interest rate we need to applied the RATE formula which is shown in the attached spreadsheet

Given that

Future value = 0

Present value = -$2587.09

PMT = $950

NPER = 3  years

The formula is shown below:

= RATE(NPER;PMT;-PV;FV)

The present value comes in negative

After applying the above formula, the interest rate is 5%

2)  For computing the number of years we need to use NPER i.e to be shown in the attachment below

Given that

Future Value = $920,925

Present Value  = 0

PMT = -$40,000

Interest rate = 5%

The formula is shown below

= NPER(RATE;-PMT;PV;FV)

The PMT comes in negative

After applying the above formula, the nper is 15.70 years

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