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seropon [69]
3 years ago
7

mark and kate are establsihing a fund for their son's college education. what lump sum must they deposit in an account that give

s 5% annual interest rate, compounded monthly, in order for them to have $85,000 in the fund at the end of the 10 years
Business
1 answer:
Elan Coil [88]3 years ago
8 0

Answer:

$51,608.69

Explanation:

Given that

Interest rate = 5%

Future value = $85,000

Time period = 10 years

So by considering the above information, the Present value is

= Future value ÷ (1 + interest rate)^time period

where,

Future value = $85,000

Interest rate = 5% ÷ 12 months = 0.4166%

Time period = 10 years × 12 months = 120 months

Now the present value is

= $85,000 ÷ (1 + 0.4166%)^120

= $51,608.69

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Many academic institutions offer a sabbatical policy. Every seventh year a professor is given a year free of teaching and other
Fittoniya [83]

Answer:

$ 127,773.36

Explanation:

The professor will be in sabbatical  in years 7,  14, 21, 28, 35 and 42

In each of these years, he receives full pay amounting to=50,000

The PV of the sabbatical full pay

= \frac{50,000}{1.04^7} + \frac{50,000}{1.04^14} + \frac{50,000}{1.04^21} + \frac{50,000}{1.04^28} + \frac{50,000}{1.04^35} +\frac{50,000}{1.04^42} = 84,101.22

=50,000/(1+4%)^7+ 50,000/(1+4%)^14+ 50,000/(1+4%)^21+ 50,000/(1+4%)^28+50,000

/(1+4%)^35+ 50,000/(1+4%)^42

==50,000/(1+4%)^7+ 50,000/(1+4%)^14+ 50,000/(1+4%)^21+ 50,000/(1+4%)^28+50,000

/(1+4%)^35+ 50,000/(1+4%)^42

= \frac{50,000}{1.316} + \frac{50,000}{1.732} + \frac{50,000}{2.279}  +\frac{50,000}{2.999} +\frac{50,000}{3.946} + \frac{50,000}{5.193}

=37,993.92 + 28,868.36 + 21,939.45 + 16,672.22 + 12,671.06 + 9,628.35

=  $ 127,773.36

Thus, at an interest rate of 4%, the present value of all the sabbatical earnings amount to $ 127,773.36

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