Maths B

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Kate is thinking about investing $45000 for 5 years. She deposits her money into an account which earns interest paid quarterly at a rate of 3.99% p.a. After 1½ years, Kate withdraws her investment (including interest) and deposits the full amount into a different account that pays interest at 4.29% p.a. resting semi-annually. She then leaves her investment untouched for the remainder of the 5 years.
(a) How much interest was accrued within the second year of the investment?
(b) What will be the value of Kate’s investment at the end of the five years?

  • Maths B -

    b) amount after 1½ years
    = 45000(1 + .0399/4)^6
    = 47761.31

    so for the next 3½ the above is invested at .29% pa compounded semi-annually

    final amount
    = 45000(1 + .0399/4)^6 (1 + .0429/2)^7
    = 55411.01

    a) If I read this correctly we need
    amount she has after 2 years - amount she has after 1 year

    = 45000(1 + .0399/4)^6 (1+ .0429/2)^1 - 45000(1 + .0399/4)^4
    = 48785.79 - 46822.54
    = 1963.25

    For questions like this, I usually draw a "time-line" and mark on it the different critical times and interest rates.

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