Question

pls solve this mathematically without the use of excel. thank you.

A sinking fund is set up to accumulate $70,000. The fund pays j1 = 15%. Annual deposits of $5,000 are made to the fund. (a) How much interest does the fund earn during the year between the 5th and 6th deposits? (b) How many $5,000 deposits are required? (c) What is the size of the final smaller deposit? (Explain your answer).

Answer 1

The answers to your questions are as follows:
(a) value at the end of 6th year - sooo & (tous) (15 13 o souo „1915-1 a sovo x 7.753738438 2 387 68 692 value at the aund of 5th year. 4 C e sooo {15 TS-S a & CINDES = 3000 x 5.74238125- s 28711.go. - 2007k go. B89768.698. son interest between the 6th deposits - $ (3.87681692 - 28711-90.-soro ) = $ 8056.792

(6 Let, it takes 'n' years to get $ TOODO, So, 40,000 - 5000 (140.15744 (+ 0.15 ... (115) - Sono x 15 or 70000 x 0 15 (115)" - 13 5000 or (1.15 h = 1.8261 or, (1.1596296 28261 or (n) log (1.15) = log 2.8261 or no 8.433043.7.433043 So,xe,,$ 5000 deposite are required. (e) Só, amount accumulated after 18 years = $5000 Sl (1+0.16385,0 0 DSA 115 . 1•15-1 s $ 63634,09542 Now, If & x is given in the last payment (636340095429 +x)(1-15). Foodo, (63634.09542 +%) 70,000 TOBBER 2016 x =$-2764530 .. Last installment not to be paid, it' u be zero, & fund will generate before the completion of the last year (8th year).