Christine O?Brien, who is self-employed, wants to invest S80,000 in a pension pl

Question

Christine O?Brien, who is self-employed, wants to invest S80,000 in a pension plan. One investment offers 1% compounded quarterly. Another offers 6.75% compounded continuously. a. Which investment will earn the most interest in 6 years? b. how much more will the better plan earn? c. What is the effective rate in each case? d. If Ms. O?Brien chooses the plan with continuous compounding, how long will it take for her $80,000 to grow to $90,000? e. how long will it take for her 580,000 to grow to at least S90,000 if she chooses the plan with quarterly compounding? (Be careful; interest is added to the account only every quarter.)

Explanation / Answer

Compounded quaterly: A = P (1 + r/4)4t

A = 80,000 (1 + 0.07/4)4(6)

A = $ 121,315.4229

Compounded continously : A = P ert

A = 80,000 e(0.0675)(6)

A = $ 119,944.2

So, quaterly plan is better by $ 1,371.223

c)Effective rate for investment compounded quarterly = (1 + 0.07/4)4 - 1 = 7.186%

Effective rate for investment compounded continuously = e0.0675 - 1 = 6.98%

d) A = 90,000, P = 80,000, r = 0.0675

90,000 = 80,000 e(0.0675)t

0.0675 t = ln(9/8)

t = 1.745 years

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