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?
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?
