Question

a) Calculate the accumulated value after 6 month of an investment of kshs 1,000 at time t=0 at the following rate of interest

i) A force of interest of 0.05%

ii) A rate of interest of 5% per annum

convertible monthly

iii) An effective rate of interest of 5% per

annum

b) Given an investment of kshs1,000,000. Find the accumulation after 5years using:

I) simple discount of 8% per annum

II) compound discount of 8% per annum

III) compound interest of 8% per annum

Answer 1

a)

i) find the formula:

$PV\times e^{y\timesδ} = FV$

PV=1000

δ=0.0005

y=0.5

$1000\times e^{0.5\times0.0005} = 1000.25$

ii)find the formula:

$FV = PV(1 + i)^ⁿ$

PV=1000

i=0.00417

$i=\frac{iy}{12}=\frac{0.05}{12}=0.00417$

$FV = 1000(1 + 0.00417)^6=1025.28$

iii)let's convert the effective bid to the nominal one

find using the formula:

$re=(1+\frac{i}{n})^n-1$

$0.05=(1+\frac{i}{12})^{12}-1$

i=0.0512

$FV = PV(1 + i)^ⁿ=1000(1+0.0512)^6=1349.31$

b)

i) find the formula:

$FV=\frac{PV}{(1-r\times n)}$

PV=1000 000

r=0.08

n=5

$FV=\frac{1 000 000}{(1-0.8\times 5)}=1 041 666.67$

ii)find the formula:

$FV=\frac{PV}{(1-r)^n}$

PV= 1000 000

r=0.08

n=5

$FV=\frac{1 000 000}{(1-0.08)^5}=1 517 262.99$

iii)find the formula:

$FV = PV(1 + i)^ⁿ$

PV= 1000 000

i=0.08

n=5

$FV = 1 000 000(1 + 0.08)^5=1 469 328.08$