Maths B
posted by Tee on .
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 semiannually. 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?

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 semiannually
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 "timeline" and mark on it the different critical times and interest rates.