Annuity due.   Reginald is about to lease an apartment for 12 months. The landlord wants him to make the lease payments at the start of the month. The monthly payments are ​$1 comma 300 per month. The landlord says he will allow Reg to prepay the rent for the entire lease with a discount. The​ one-time payment due at the beginning of the lease is ​$14 comma 778 . What is the implied monthly discount rate for the​ rent? If Reg is earning 1.5 ​% on his savings​ monthly, should he pay by month or make the​ one-time payment?

a. The implied monthly discount rate for the rent is 0.843% (10.115%/12)

b. He should pay by month because he will earn 1.5% on his savings and pay 0.843% interest monthly.

Explanation:

a) Monthly payments at the start of the month = $1,300

One-time payment at the beginning of the lease = $14,778

Present Value  14778

Residual Value  0

Lease Term  0  years  12  months

Monthly Payment  1300

Result

Interest/Return Rate10.115%

Total of 12 Monthly Payments$15,600.00

Total Interest$822.00

If Reg is earning 1.5% on his savings monthly, he will earn $21,957:

Annuity factor for 12 months at 1.5% = 16.89

Total of Reg's savings at the end of 12 months = $21,957 ($1,300 * 16.89)

you will have $2593.74 in 10 years if you set aside $1,000 at 10%

you will have $9321.91 in 20 years if you set aside $2000 at 8%

you will have $1469.32 in 5 years if you set aside $1000 at 8%

you will have $1296.87 in 10 years if you set aside $500 at 10%

you will have $239.66 in 15 years if you set aside $100 at 6%

you will have $4660.96 in 20 years if you set aside $1000 at 8%