time payment qn (1 Viewer)

[bos1234]

 

[PC]

(b) $67275.00
(c) $572749.99

 

[bos1234]

Could you please show the working?

b) is right but c) says 630 025?

 

[PC]

It might depend on when the interest is paid. Is interest paid at the start of each period, on 1 January, or is it paid at the end of each period, on 31 December?

Working?

The 1st $10000 is invested at 10% p.a. for 20 years.
The 2nd $10000 is invested at 10% p.a. for 19 years.
The 3rd $10000 is invested at 10% p.a. for 18 years.
The final $10000 is invested at 10% for 1 year.

.: A1 = 10000(1 + 0.10)²⁰ = 10000(1.1)²⁰
.: A2 = 10000(1 + 0.10)¹⁹ = 10000(1.1)¹⁹
.: A3 = 10000(1 + 0.10)¹⁸ = 10000(1.1)¹⁸
.: A20 = 10000(1 + 0.10)¹ = 10000(1.1)¹

.: Total = A1 + A2 + A3 + ... + A20
= 10000(1.1)²⁰ + 10000(1.1)¹⁹ + 10000(1.1)¹⁸ + ... + 10000(1.1)¹
= 10000(1.1¹ + 1.1² + 1.1³ + ... + 1.1²⁰)
= 10000 x [ 1.1 (1.1²⁰ – 1) / (1.1 – 1) ]
= 10000 x 63.00249944
= $630 024.99

 

[bos1234]

ok thanks