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