Engineering Economic Analysis

Continu_ous C~mpounding 117

To find compound amount and present worth for continuous compounding and a single

payment, we write:

Compoundamount

Present worth

F= P(ern)= P[F/P, r, n]

P= F(e-rn)= F[P/F, r, n]

(4-39)

(4-40)

Square brackets around the factors distinguish continuous compounding. If your hand cal-

culator does not haveeX,use the table ofernande-rn,provided at the end of the appendix

containing the compound inter~st tables.

~_$~;~~~~r'~"

If you were to deposit $2000 in a bank that pays 5% nominal interest, compoundedcontinuously,

how much would be in the account at the end of 2 years?

The single payment compound amount equation for continuous compounding is

where r=nominal interest rate=0.05

n=number of years = 2

F=2000e(O.05)(2) =2000(1.1052) =$2210.40

There would be $2210.40 in the account at the end of 2 years.
.......

A bank offers to sell savings certificatesthat will pay the purchaser $5000 at the end of 10 years
but will pay nothingto the purchaserin the meantime.If interest is computed at 6%, compounded
continuously,at what price is the bank selling the certificates?

F=$5000 r=0.06 1'J=10 years

P= 5000e-O.06xlO= 5000(0.5488) = $2744

TherefQre,the bank is selling the $5000 certificatesfor $2744.