Question

8. At what quoted annual interest rate must $135,000 be invested so that it will grow to be $460,000 in 15 years if interested is compounded weekly?

9. If you wish to accumulate $500,000 in 20 years, how much must you deposit today in an account that pays a quarterly interest rate of 2%?

10. How many months will it take for $200,000 to grow to be $550,000 if it is invested in an account with a quoted annual interest rate of 8% with monthly compounding of interest?

Answer #1

8.

Present value be PV = 135000

Number of investment periods = n = 15*52 = 780 weeks

Future Value after 15 years = 460000

Let Annual Interest rate be r => Weekly Interest Rate = r/52

We know that FV = PV(1+r)^{n}

=> 460000 = 135000(1+r/52)^{780}

=> r = 52 * [(460000/135000)^{1/780} - 1 ] = 0.0818
or 8.18%

9. Quarterly Interest Rate = r = 2%

Number of periods = n = 20*4 = 80 quarters

Future Value Required = FV = 500000

Let present investment required be PV

We know that FV = PV(1+r)^{n}

=> 500000 = PV(1+0.02)^{80}

=> PV = 500000/(1+0.02)^{80} = $102554.86

10.

Given,

Present Value = PV = 200000

Future Value = FV = 550000

Annual Interest Rate = 8%

Monthly interest Rate = 0.08/12

Let the number of months be n

We know that FV = PV(1+r)^{n}

=> 550000 = 200000(1+0.08/12)^{n}

=> 550000/200000 = (1+0.08/12)^{n}

Taking natural log of both sides

=> n = ln (550000/200000)/ ln (1+0.08/12) = 152.24 months

Please show your work. If you don't show your work, you
will not get credit. You can put the number next to the function in
your submission. For example, FV = 150,000, PV = 250,000, i = 10%,
and n = 5. Questions, let me know. If you do not show your work, no
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