EXAMPLES. I What annuity or yearly rent, to continue 6 years may be purchased for 1017 10s 3d 3qrs at 5 per cent? Ans. 201 2 Suppose the present payment of 133! 11s id were required for a pension for 5 years to come, at 4 per cent. what is that pension? Answer 30% per ann. 3 If the present payment of 1857 17s 1d 2qrs. be made for the lease of a house, 4 years to come, at 3 per cent. what is the yearly rent? Answer 50 per annum. 4 If a house is let upon lease for 4 years, and the lessee makes present payment of 2431 19s od 3qrs for that time at 5 per cent. what is the yearly rent of the house? Ans. 70l per ann. CASE 3. Q. When U, P, and R, are given to find T, how is it discovered ? EXAMPLES. 1 How long may a lease of 201 yearly rent be had for 104/ 10s 3d 3qrs allowing 5 per cent to the purchaser ? Answer 6 years. 2 I demand what time a lease of 301 per annum may be purchased for; when present payment of 133 11s id is made at 4 per cent? Answer 5 years. 3 If 185 17s 1d qrs. be paid down for a lease of 501 per annum at 3 per cent. how long is the lease purchased for? Answer 4 years. 4 A house is let upon lease, at 70 per annum and the lessee makes present payment of 2431 19s od 3qrs he being allowed 53 per cent. I demand how long the lease is purchased for? Answer 4 years. OF ANNUITIES, LEASES &c. TAKEN IN REVERSION. CASE 1. Q. How many operations are there in Case 1? Q. What is the first? A. Find the present worth of the yearly sum at the given rate, and for the given time of its continuance; to do which there are given U, T, and R, to find P. Q. What is the Second ? A. Find what principal being put to interest will amount to P, at the same rate, and for the time to come before the annuity commences, and that will be the present worth of the annuity, &c. In Reversion; therefore let P be chang ed into A=the amount, and then there will be given A, R, and T, to find P, or the Principal. Q. How is P discovered? A. Thus ; α t r EXAMPLES. 1 What is the present worth of the Reversion of a Lease of 201 per ann. to continue 4 years, but not to commence till the end of two years, allowing 5 per cent to the purchaser ? Ans. 64/ 6s 6d 1.4+qrs. 2 There is a lease of certain lands worth 321 per ann. which is yet in being for 4 years; and the Lessee is desirous to take a Lease in Reversion for 7 years, to begin when the old Lease shall be expired; I demand the present worth of the said Lease in Reversion, allowing 5 per cent to the purchaser? Ans. 152/ 6s 8d 2grs+. 3 There is a house now building, which I have a mind to take a Lease of for 8 years; but the house will not be finished within two years: I demand how much I must pay down, when the yearly rent is 1007 and the landlord allows me 4 per cent on present payment? Ans. 6221 9s 7.2d CASE 2. Q. How many operations are there in Case 2? Q. What is the first? A Find the amount of the present worth of the yearly sum at the given rate, and for the time before the annuity commences, to do which there are given P, R, and T, to find A. Thus pra Q. What is the second? A. Find what yearly rent being sold will produce A for the present worth at the same rate, and for the time of its continuance; and that will be the yearly sum required: therefore let A be changed into P, and then there will be given P, R, to find U, or the yearly sum. 1 What annuity or yearly rent to be entered upon 2 years hence, and then to continue 4 years, may be purchased for 641 6s 6d 2qrs ready money, at 5 per cent. ? Answer 201. 2 There is a Lease of certain lands in being for 4 years, and the Lessee being minded to take a Lease in Reversion for 7 years, to begin when the old Lease shall be expired, laid down 152 6s 8d 2qrs. I demand the yearly rent of the said lands, when allowance was made to the Lessee, at 5 per cent? Ans. 321 per ann. 3 The present payment for the Lease of a house is 622/ 9s 7.2d. Now I have taken a Lease in Reversion for 8 years, which is to commence at the end of two years; I demand how much the yearly rent is, when for the said present payment I was allowed 4 per cent ? Ans. 100 per ann. CASE 3. Q. How many Operations are there in Case 3? A. Two. Q. What is the First P A. Find the amount of the present worth of the yearly sum at the given rate, and for the time before the annuity, e. commences; to do which there are given P, R, and T, to find A, as in Case 2. Q. How is A discovered? A. Find what time the yearly rent given being sold for will produce A for the present worth, at the same rate, and that will be the time required: therefore echange A into P, and then there will be given U, P, and Ry to find T, as in Case 3, page 164. Q. How is T discovered ? 1 The present worth of a certain Lease in Reversion is 647:6s 6d 2qrs the Lease is 201 per annum and commences 2 years hence, and the allowance to the purchaser is 5 per cent. I demand the time of its continuance? Answer 4 years. 2 A certain man took a Lease of some Lands, for a time, which by agreement was not to commence till the expiration of 4 years; the yearly rent was 321 it was also agreed, that the purchaser should lay down 152/ 6s 3d 2 qrs. and be allowed for his present pay at 5 per cent. I demand the time that the Lease was taken for? Answer 7 years. 3 The present payment for the Lease of a house is 6221 9s 7.2d. and the yearly rent is 100l. Now I have taken a lease in reversion, which is to commence at the end of two years; I demand the length of the lease, when I was allowed 4 per cent. for my Money? Answer 8 years. + OF PURCHASING REAL OR FREEHOLD ESTATES. Q. What do you understand by a Real or Freehold estate? A. Such as is bought to continue for ever. Note. U represents the yearly rent; R, the amount of 11. &c. and P the present worth. CASE 1. Q. When U, and R, are given to find P, how is it dis covered? A. Thus ; EXAMPLES. 1 Suppose a Freehold Estate of 40l per annum is to be sold, what is it worth, allowing the buyer 5 per cent for his money ? Ans. 8001. 2. What is an Estate of 2901 per ann. to continue for ever worth in present money, allowing 4 per cent. to the Buyer Ans. 72501. CASE 2. Q. When P, and R, are given to find U, how is it discovered ? A. Thus; p+r—1=u EXAMPLES. 1 If a Freehold Estate is bought for 800l and the allowance of 5 per cent. is made to the buyer; I demand the yearly rent? Ans. 401 per ann. 2 If an estate be sold for 7250 present money, and 4 per cent. is allowed to the buyer for the same; I demand the yearly rent? Ans. 2901 per ann. CASE 3. Q. When P, and U, are given to find R, how is it discovered? 1 If a real estate of 407 per ann. be sold for 800%. I demand the rate per cent. ? Ans. per cent. 2 If a Freehold Estate of 290l per ann. be bought for 72501. I demand the rate per cent. allowed? Ans. 4 per cent. OF PURCHASING FREEHOLD ESTATES IN REVERSION. Q. How many operations are there in Case 1 ? A. Two. Q. What is the First? A. Find the present worth of the yearly sum at the given rate, to do which there are given U, and R, to find P. Q. What is the second operation? A. Find what principal being put to interest will a |