Analysis and Approaches for IBDP Maths Ebook 1 | Page 75

Front Page
Exercise 24
1. On 1st January 2030, Zoe invests $P in an account that pays a nominal annual interest
rate of 3.7%, compounded quarterly. The amount of money in her account at the end of
each year follows a geometric sequence with common ratio R .
(a)
Find the value of R , giving the answer to five significant figures.
It is given that there is no further deposit to or any withdrawal from the account.
[3]
(b)
Find the year in which the amount of money in Zoe’s account will become three
times the amount she invested.
[3]
2. On 1st July 2021, Jane invests $180000 in an account that pays a nominal annual interest
rate of 5.1%, compounded monthly. The amount of money in her account at the end of
each year follows a geometric sequence with common ratio R .
6
(a)
Find the value of R , giving the answer to five significant figures.
It is given that there is no further deposit to or any withdrawal from the account.
[3]
(b)
Find the year in which the amount of money in Jane’s account will become
$400000.
[3]
3. Aaron invested $P dollars in an account that pays a nominal annual interest rate of 2.9%,
compounded quarterly. After 7 years he has $2300 in the account.
(a)
Find the value of P , giving the answer to three decimal places.
Aaron then bought a cup that cost $2300 and sold it 5 years later for $200.
[3]
(b)
Find the rate at which the cup depreciated per year.
[3]
4. Xenia invested $P dollars in an account that pays a nominal annual interest rate of 7.3%,
compounded monthly. After 9 years she has $290000 in the account.
(a) Find the value of P , giving the answer to the nearest integer.
[3]
Xenia then bought a car that cost $290000 and sold it t years later for $205000. The rate
at which the car depreciated per year is 6.25%.
(b) Find the value of t .
[3]
www.seprodstore.com
67