Simple Interest

EXERCISE 01

€2,000 is invested for eight months at 9% per year. Use simple interest.

A.Calculate interest and the accumulated amount.

A.

I=Cit,\qquad M=C(1+it)

t=\frac{8}{12}\text{ years}

I=2{,}000(0.09)(8/12)=120.00

M=2{,}000+120.00=2{,}120.00

Simple Interest

EXERCISE 02

€5,000 is invested for ten months at 4% per two-month period. Use simple interest.

A.Calculate interest and the accumulated amount.

A.

I=Cit,\qquad M=C(1+it)

t=\frac{10}{2}=5\text{ two-month periods}

I=5{,}000(0.04)(10/2)=1{,}000.00

M=5{,}000+1{,}000.00=6{,}000.00

Simple Interest

EXERCISE 03

€20,000 grows to €21,500 at 10% annual simple interest. Use twelve equal months per year.

A.Find the investment duration.

A.

t=\frac{M/C-1}{i}

t=\frac{21{,}500/20{,}000-1}{0.10}=0.75

0.75 years = 9 months.

Simple Interest

EXERCISE 04

€15,000 earns simple interest for four months at 12% per year and then six months at 2% per quarter. Interest is not capitalised at the rate-change date: both stages use the original principal.

A.Calculate the final accumulated amount.

A.

M=C\left(1+\sum_k i_kt_k\right)

I_1=15{,}000(0.12)\frac4{12}=600

I_2=15{,}000(0.02)\frac6{3}=600

M=15{,}000+600+600

€16,200.00

If the first-stage interest were reinvested instead, the amount would be €15,000 × 1.04 × 1.04 = €16,224. That is a different, explicitly capitalised arrangement.