Question

A worker invests £1000 at the end of each year for 10 years in a project that grows at an annually compounded rate of 6%.

1. Calculate the terminal value of the investment? [4]
2. By what factor would your answer to (i) change if the investments were made at the beginning of the year? [1]  
3. Use your answer to (i) to work out the principal, P that could be borrowed for 10 years at a compounded rate of 6% with equal, end of year annual repayments of £1000. [3]

Answer 1

Solution :-

(i)

Rate of Interest = 6%

Annual Deposit = $1,000

Time = 10 Years

Terminal Value of Investment = $1,000 * PVAF ( 6% , 10 )

= $1,000 * [ ( 1 + 0.06 )¹⁰ - 1 ] / 0.06

= $16,666.67 * [ 1.7908 - 1 ]

= $13,180.79

(ii) If the Payment Deposit in the beginning of the Year

Future Value = $1,000 * FVAF ( 6% , 10 ) * ( 1 + 0.06 )

= $1,000 * [ ( 1 + 0.06 )¹⁰ - 1 ] * 1.06 / 0.06

= $13,180.79 * 1.06

= $13,971.64

Answer changed by $13,971.64 - $13,180.79 = $790.85

(iii)

The Amount that need to be borrowed today to pay $1,000 for 10 Years

= $1,000 * PVAF ( 6% , 10 )

= $1,000 * [ 1 - ( 1 + 0.06)^-10 ] / 0.06

= $16,667 * [ 1 - 0.5583 ]

= $7,360.09

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