In: Finance
In December Beth bought a boat for $100,000 & payed $16,000 down & agreed to pay the balance In 5 equal annual installments that include both the principal & 9% interest on the declining balance. How big will the annual payments be?
Beth bought the yacht for $100,000 & paid $16,000 down, how much doe she need to borrow for her purchase of the yacht?
$__ (round to the nearest dollar)
1. Annual payments be := $21595/-
Working Note
This sum can be calculated using time value of money concept using following formula.
Equated annual installment = Loan amount/ PVIFA(r ,n)
= 84000 / PVIFA(9%,5)
= 84000 / 3.890
= $21595/-
Note : PVIFA has been seen from Present value of annuity table using rate 9% and n=5 used for calculating time value of money.
Loan amount = Cost of Boat -Down Payment
= $100000-$16000 =$84000
2. beth needs to borrow following amount based below mention on loan Amortisation schedule:
Year |
Beginning Amount |
Annual Installment |
Interest |
Principal Repaid |
Remaining Balance |
1 | 84000 | 21595 | 7560 | 14035 | 69965 |
2 | 69965 | 21595 | 6297 | 15298 | 54667 |
3 | 54667 | 21595 | 4920 | 16675 | 37992 |
4 | 37992 | 21595 | 3419 | 18176 | 19816 |
5 | 19816 | 21595 | 1783 | 19812 | 5 |
Total | 23980 | 83995 |
Amount needs to borrow = &84000+$23980 =$107980
Note: Most of financial institutions allow borrowings upto 85% of loan amount depends on institutes loan policy they may also allow to borrow processing fees too.