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?
(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?
Answers
Reiny
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.
= 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.