Question

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?

Answer 1

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.