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IBM Mathematics 1 Financial Mathematics
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1) A lent B an amount of 650 € on January 1, 1995. B undertakes to borrow the amount with 7% easy interest.The repayment becomes due on December 31, 2004. How tall is it amount to be refunded?
r=7%=0.07 T=10 C0=650 C T =C 0 ( 1+ r∗T )=¿ 650 ( 1+0.07∗10 ) =1105
2) An amount of 1200€ was invested at 5% with simple interest and, together with the accrued interest it has
grown to currently 1620 €. How many years was the amount invested?
CT 1620
−1 −1
r=5%=0.05 C0=1200 CT=1620 C0 1200
T= =¿ =7
r 0.05
3) An amount of 3200 € was invested at simple interest for 8 years and is increased to 4736€ during this period
including interest paid. What was the underlying interest rate r?
CT
−1 4736 −1
T=8 C0=3200 CT=4736 C0 3200
r= = =0.06=6 %
T 8
4) At what percentage of annual interest is the stake tripled Investment amount in 10 years if compound
interest is assumed?
CT=3 C0=1 T=10 T
C T =C 0 (1+r ) =¿ r=
√
T CT
C0
−1=
√
10 3
1
−1= √ 3−1=1.116−1=0.116=11.6 %
10
5) In how many years will an investment amount triple at 5.37% annual interest if we assume interest with
compound interest?
CT=3 C0=1 r=5.37%=0.0537 T =log ¿ ¿
6) What is the present value of a payment of 6000€ made exactly 11 years from now with an assumed interest
rate of 8% p.a. and annual compound interest?
−T −11
ZT=6000 T=11 r=8%=0.08 B0=Z T ∗( 1+ r ) =6000∗( 1+ 0.08 ) =2573.2971
7) A merchant expects • in exactly one year through the sale of property A, an amount of 225 000€ to redeem,
and • in exactly four years through the sale of property B, an amount of 410 000€ to redeem. Assume that
the merchant's expectations will be met exactly. What is the present value of the total of these two
payments when calculating based on an interest rate of 4% p.a., with annual compound interest?
−T −1
ZT=225 000 T=1 r=4%=0.04 B0=Z T ∗( 1+ r ) =225 000∗(1+ 0.04 ) =216346.1538
−T −4
ZT=410 000 T=4 r=4%=0.04 B0=Z T ∗( 1+ r ) =410 000∗( 1+0.04 ) =350469.7183
Total = 216346.1538 + 350469.7183 = 566815.8721
8) For short-term fixed deposits, XYZ-Bank grants an interest rate of 0.3% per month with simple interest. A
private investor wants invest 81,000€ for 40 days. What amount will be repaid to the investor at the end of
the term? Note: For simplicity, assume that the equation 1 year = 360 days when calculating interest.
r=0.3%=0.003=>0.003*12=0.036 T=40=>40/360=1/9
(
C T =C 0 ( 1+ r∗T )=¿ 81 000 1+
0.036∗1
9 )=81324
9) A merchant grants one of his employees to bridge a short-term financial bottleneck. A loan of 800€ at an
interest rate of 0.02% per day with simple compounding. What amount does the employee pay after 45
days back?
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