i have three equations: 1. A young man is the beneficiary of a trust fund establ

Question

i have three equations: 1. A young man is the beneficiary of a trust fund established for him 18 yr ago at his birth. If the original amount placed in trust was $40,000, how much will he receive if the money has earned interest at the rate of 7%/year compounded annually? Compounded quarterly? Compounded monthly? (Round your answers to the nearest cent.)

compounded annually $

compounded quarterly $

compounded monthly $

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2. Find the effective rate of interest corresponding to a nominal rate of 4%/year compounded annually, semiannually, quarterly, and monthly. (Round your answers to two decimal places.)

annually %

semiannually %

quarterly %

monthly %

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3. Maria, who is now 45 years old, is employed by a firm that guarantees her a pension of $35,000/year at age 65. What is the present value of her first year's pension if the inflation over the next 20 years is 6%/year compounded continuously? 8%/year compounded continuously? 12%/year compounded continuously?

(Round your answers to the nearest cent.)

at 6%/year $

at 8%/year $

at 12%/year $

Explanation / Answer

Answer:1 compounded annually:

A=$40000*(1.07)18

=$135197.2910

Compounded monthly:

A=$40000*(1+7%/12)18*12

=$40000(1.005834)216

=140500.5671

compounded quarterly:

A=$40000*(1+7%/4)18*4

=$40000(1.0175)72

=139488.3958

Answer:2

reff=(1+r/m)m-1

annually=(1+4%/1)1-1

=(1.04)1-1

=4%

semiannually:(1+4%/2)2-1

=(1.02)2-1

=4.04%

Quarterly: (1+4%/4)4-1

=(1.01)4-1

=4.06%

Monthly: (1+4%/12)12-1

=(1.003333)12-1

=4.073%

Answer:3

A = Pe^(rt)
A / e^(rt) = P

35000 = Pe^(.06 * 20)
35000 / e^1.2 = P

35000 = Pe^(.08* 20)
35000 / e^1.6 = P

35000 = Pe^(.12 * 20)
35000 / e^2.4= P

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