Date | May 2021 | Marks available | 3 | Reference code | 21M.1.SL.TZ2.10 |
Level | Standard Level | Paper | Paper 1 | Time zone | Time zone 2 |
Command term | Determine | Question number | 10 | Adapted from | N/A |
Question
Tommaso and Pietro have each been given 1500 euro to save for college.
Pietro invests his money in an account that pays a nominal annual interest rate of 2.75%, compounded half-yearly.
Calculate the amount Pietro will have in his account after 5 years. Give your answer correct to 2 decimal places.
Tommaso wants to invest his money in an account such that his investment will increase to 1.5 times the initial amount in 5 years. Assume the account pays a nominal annual interest of r% compounded quarterly.
Determine the value of r.
Markscheme
METHOD 1
N=5 OR N=10
I%=2.75 I%=2.75
PV=-1500 PV=-1500
PMT=0 PMT=0
P/Y=1 P/Y=2
C/Y=2 C/Y=2 (M1)(A1)
Note: Award M1 for an attempt to use a financial app in their technology, A1 for all entries correct.
METHOD 2
1500(1+2.752×100)2×5 (M1)(A1)
1719.49 euro A1
[3 marks]
METHOD 1
N=5 OR N=20
PV=±1500 PV=±1500
FV=∓2250 FV=∓2250
PMT=0 PMT=0
P/Y=1 P/Y=4
C/Y=4 C/Y=4 (M1)(A1)
Note: Award M1 for an attempt to use a financial app in their technology, A1 for all entries correct. PV and FV must have opposite signs.
METHOD 2
1500(1+r4×100)4×5=2250 OR (1+r4×100)4×5=1.5 (M1)(A1)
Note: Award M1 for substitution in compound interest formula, A1 for correct substitution and for equating to 2250 (if using LHS equation) or to 1.5 (if using RHS equation).
r=8.19 (8.19206…) A1
Note: Accept r=8.19%.
Accept a trial and error method which leads to r=8.19.
[3 marks]