Question

Judy Dench took up the government offer on the “Special Early Retirement Programme” and received a lump sum payment of J$3.5M. After clearing her mortgage and credit card debts she has J$1.5M remaining. She saw an advertisement recently in the local newspaper where JMMB was offering three investments offer to the public as follow:

Investment Product	Interest Rate	Term	Conditions
Investment A	16%	5 years	Interest is compounded annually. Principal & Interest is paid at the end of the 5 years.
Investment B	13.80%	6 years	Interest is compounded annually. Principal & Interest is paid at the end of the 6 years.
Investment C	11.60%	7 years	Interest is compounded annually. Principal & Interest is paid at the end of the 7 years.

If Judy wants to invest only J$1,000,000; which one of the investment products based on calculations would you recommend her to invest in?                                                       

B. John Travolta plans on investing the following cash flows at the beginning of each year:

            Year                Cash Flow

            2019                $30 000

            2020                $40 000

            2021                $60 000

            2022                $90 000          

            2023                $20 000

How much would John accumulate at the end of 2023 if the interest rate is compounded annually at an interest rate of 9.8%?

Answer 1

(A)

Investment Project A:

GIVEN:

Principal (P) = $10,00,000

Interest rate (r) = 16% = 0.16

no. of times compounded annually: 1

term (t) = 5 years

FORMULA :

A = P (1 + r / n) nt

A = 10,00,000 ( 1+ 0.16/ 1)1*5

=  10,00,000 ( 1.16)5

= 10,00,000 (2.100341658)

= $ 21,00,341.658

Investment Project B:

GIVEN:

Principal (P) = $10,00,000

Interest rate (r) = 13.80% = 0.138

no. of times compounded annually: 1

term (t) = 6 years

FORMULA :

A = P (1 + r / n) nt

A = 10,00,000 ( 1+ 0.138/ 1)1*6

=  10,00,000 ( 1.138)6

= 10,00,000 (2.17196875)

= $ 21,71,968.75

Investment Project C:

GIVEN:

Principal (P) = $10,00,000

Interest rate (r) = 11.60% = 0.116

no. of times compounded annually: 1

term (t) = 7 years

FORMULA :

A = P (1 + r / n) nt

A = 10,00,000 ( 1+ 0.116/ 1)1*7

=  10,00,000 ( 1.116)7

= 10,00,000 (2.156003007)

= $ 21,56,003.007

The best investment plan for Judy is Project B which yields $1,171,968.75 interest and gives her a total amount of $ 21,71,968.75 at the end of 6th year.

(B)

given:

rate of interest (r) = 9.8%= 0.098

term (t) = 1

no. of times compounded (n) = 1

solution:

At year 2019: John invests $30,000 at interest rate 9.8%

A = P (1 + r / n) nt

=30000 (1+ 0.098/1) 1*1

= 30,000 * 1.098

= $32,940

at the end of 2019 John will have : $32,940 in his bank acccount

John invests another $40000 at the starting of 2020.

therefore p= $32,940 + $40000= $72940

A = P (1 + r / n) nt

= 72,940 ( 1+ 0.098/1) 1*1

= 72,940 * 1.098

= $80,088.12

at the end of 2020 John will have : $80,088.12 in his bank acccount.

At the beginning of 2021 another 60000 is invested

p= 80,088.12 + 60000= 1,40,088.12

A = P (1 + r / n) nt

= 1,40,088.12 ( 1+ 0.098/1) 1*1

= 1,40,088.12 * 1.098

= $153,816.76

at the end of 2021 John will have : $153,816.76 in his bank acccount.

At the beginning of 2022 another 90000 is invested

p= $153,816.76 + 90000= $2,43,816.7558

A = P (1 + r / n) nt

= 2,43,816.7558 ( 1+ 0.098/1) 1*1

= 2,43,816.7558 * 1.098

= $267,710.80

at the end of 2022 John will have : $267,710.80 in his bank acccount.

At the beginning of 2023 another 20000 is invested

p= $267,710.80 + 20000= $287,710.80

A = P (1 + r / n) nt

= 287,710.80 ( 1+ 0.098/1) 1*1

= 287,710.80 * 1.098

= $315,906.46

at the end of 2023 John will have a total amount of $315,906.46 in his account.