Question

A person deposits $100 at the beginning of each year for 20 years. Simple interest at an annual rate of i is credited to each deposit from the date of deposit to the end of the twenty year period. The total amount thus accumulated is $2840. If instead, compound interest had been credited at an effective annual rate of i, what would the accumulated value of these deposits have been at the end of 20 years

Answer 1

Answer:

Future value if compounding interest: $3,096.9202

Explanation:

The simple interest do not consider that interest generate more interest like compounding. It considers the investor withdraw their return rather than reinvesting.

$FV = PMT \times time \left[1+rate \times\frac{time + 1 }{2} \right]$

100 x 20 x (1 + i x (20+1)/2) = 2,840

(2,840/2,000 -1) x 2 / 21

r = 0.04

Now, we solve considering compounding which assume all interest are reinvested.

$C \times \frac{(1+r)^{time} -1}{rate}(1+r) = FV$

C 100.00

time 20

rate 0.04

$100 \times \frac{(1+0.04)^{20} -1}{0.04}(1+0.04) = FV$

FV $3,096.9202