Question

(a) Payments of RM 100 are made continuously throughout the year for 8 years and interest is credited at a constant force of interest, 8, of 5%. Calculate the future value of these payments at the end of 8 years. (b) Now assume a payment of RM 100 is made continuously throughout the first year, a payment of RM 200 is made continuously throughout the second year, and so on until a payment of RM 800 is made continuously throughout the eighth year. Calculate the present value of this annuity if 8 is a constant 5%.

Answer 1

(a)Future Value of payments of RM 100 for 8 years @ 5% has to be calculated as below.

$\int_{0}^{8}100 e^{^{^{}}}(.05(8-x) )$ dx

= 983.6493952825406