REVERSIONS. 
53 
(1 
+ 
d(l + î')- (d+1) + ^ 
a 
29720936 
.0033, 
i = .03 + .0033 = .0333 
100 
3.33 per cent. 
RENEWAL OF LEASES. 
68. The fine to be required for renewing any number of years ex 
pired in a lease will be the present value of an annuity deferred for the 
unexpired term of the lease, and then to continue for the period re 
newed ; we have therefore the following rule : 
Rule. From the present value of an annuity to continue from the 
present time until the expiration of the renewed term subtract the 
present value of an annuity to expire with the original term of the lease. 
Example. Fifty years having expired in a lease for the term of 60 
years, what sum should be paid for renewing them, supposing the estate 
to produce a clear rental of £90 per annum, and the interest of money 
5 per cent? 
By Table 6,—the value of £l per annum for 60 years is 18.9293 
ditto for 10 years, the unexpired term 7.7217 
11.2076 
90 
£1008 13 8 1008.684 
Example 2. Thirty years having expired in a lease for 40 years, 
required to know the fine for renewing 10 years of the same, supposing 
the yearly rental £60, and the rate of interest 5 per cent. 
40 — 30 = 10 = unexpired time, 
10 + 10 = 20 = number of years until the expiration of the 
renewed term. 
By Table 6,—the value of £l per annum for 20 years 12.4622 
ditto, for 10 years, the unexpired time 7.7217 
~i77405 
60 
£284 8 7 284.430~ 
69. The following Tables show the number of years’ purchase that 
ought to be paid at different rates of interest for the renewal of any 
number of years lapsed in a lease for the original term of 10, 20, 21, 
and 40 years ;