Question

A medical insurance company has offered to pay you a medical refund today of K350, 000.00 or to pay K650, 000.00 in three years time. If interest rates in the market were 20% compounded semi annually which of the two options would be worthwhile? 

If you planning to invest some funds in the following manner; K20,000 at the end year 1,K30,000 at the end of year 2 and K10,000 at the end of year 3.How much would this account have at the end of year 4 assuming the funds earn interest of 12% compounded per annum? 

You have inherited two endowment funds from your grandfather. One fund will pay K30, 000.00 annually indefinitely, while the other fund will pay K12, 000 annually for 20years.The insurance company has offered to buy this fund from you. Calculate the combined market value on such fund if interest were 18% in the market. 

An investment company offers an account which requires a one off investment of K18, 000.00 and grows to K237, 870.00 in 12 years time. Find the interest rate that the investment is offering?                                                                                    

Answer 1

1 ANS)

Let us first calculate the value of 350000 after 3 years.

The formula for annual compound interest, including principal sum, is:
A = P (1 + r/n) ^(nt)

Where:

A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for

were P= 3,50,000 r=20% or 0.2 n=2 t=3

A= 3,50,000( 1+0.2/2)^2*3

A = 3,50,000 (1.1)⁵

A = 6,20,046

Therefore the second option of receiving 6,50,000 in 3 years is worthwhile as it is more than the market return of 6,20,046.

2 ANS)

YEAR	BEGINING BALANCE		12% COMPOUND INTEREST		ENDING BALANCE
1	20000	+	20000*0.12	=	22400
2	22400+30000	+	52400*0.12	=	58688
3	58688+10000	+	68688*0.12	=	76931
4	76931+0	+	76931*0.12	=	86163

Thus Balance in the end of year 4 in the account is K86163.

3 ANS)

FUND1

A perpetuity is a type of annuity that receives an infinite amount of periodic payments. Since the fund is generating infinitely we use the perpetuity formula.

Perpetuity = Cash Flow /Interest Rate

= 30000 / 0.18

= 166666.67

FUND 2

Using the Time Value of Money formula

FV = PV (1 + r)^n

were P= 12000 r=18% or 0.18 n=1 t=20

A= 12000 (1+0.18)²⁰

^{A = 3,28,716.42}

^{Combined Market Value = Fund 1 + Fund 2}

⁼166666.67 +3,28,716.42

= 4,95,383.09

4 ANS)

Using the Time Value of Money formula and assuming interest rate as x.

FV = PV (1 + r)^n

^{237870 = 18000 ( 1+x ) 12}

x ( interest rate )= 24% 0r 0.24 ( rounded off)