1. If $5000 is invested at 7% annual simple interest, how long does it take to b

Question

1. If $5000 is invested at 7% annual simple interest, how long does it take to be worth $8150? I got 7.22 years ..that wasn't right ...
2. Find the future value of an annuity of $1100 paid at the end of each year for 15 years, if interest is earned at a rate of 6%, compounded annually. (Round your answer to nearest cent.) I got $2636.21 it was wrong.
3. Parents agree to invest $400(at 8%, compounded semiannually) for their son on the December 31 or June 30 following each semester that he makes the deans list during his 4 years in college. If he makes the deans list in each of the 8 semesters, how much money will his parents have to give him when he graduates? My answer was 740.37 wrong 1. If $5000 is invested at 7% annual simple interest, how long does it take to be worth $8150? I got 7.22 years ..that wasn't right ...
2. Find the future value of an annuity of $1100 paid at the end of each year for 15 years, if interest is earned at a rate of 6%, compounded annually. (Round your answer to nearest cent.) I got $2636.21 it was wrong.
3. Parents agree to invest $400(at 8%, compounded semiannually) for their son on the December 31 or June 30 following each semester that he makes the deans list during his 4 years in college. If he makes the deans list in each of the 8 semesters, how much money will his parents have to give him when he graduates? My answer was 740.37 wrong I got 7.22 years ..that wasn't right ...
2. Find the future value of an annuity of $1100 paid at the end of each year for 15 years, if interest is earned at a rate of 6%, compounded annually. (Round your answer to nearest cent.) I got $2636.21 it was wrong.
3. Parents agree to invest $400(at 8%, compounded semiannually) for their son on the December 31 or June 30 following each semester that he makes the deans list during his 4 years in college. If he makes the deans list in each of the 8 semesters, how much money will his parents have to give him when he graduates? My answer was 740.37 wrong

Explanation / Answer

1. If $5000 is invested at 7% annual simple interest then we know that

Amount(A) = P(1 + rt)

where P is principal, r is the rate of interest and t is time period

8150 = 5000(1+ 0.07t)
divide by 5000
1.63 = (1 + 0.07t)
then
0.63 = (0.07)t
divide ln (0.63) by (0.07) and rounding we get

t = 9 years

2. Future value of an annuity of $1100 paid at the end of each year for 15 years and interest is earned at a rate of 6%, compounded annually

FV = (1+r)*P(1+r)n-1/r
=(1+(0.06))*1100(1+0.06))15-1/0.06
=1.06*1.3965, rounding only at the end.
= $27139.78

So the future value of an annuity is  $27139.78

3. We have to assume some points here Since it's 8% compounded semi-annually, that means 4% every 6 months. Let's assume it occurs on money that has been in the account for at least 6 months.

Starting with

$400, multiply by 1.04, then add 400,

We have to do the same process of multiplying 1.04 and then adding $400 for 8 semester.

This would give us the result of $3,685.69.

This is essentially an iteration like the first person stated:

(400*1.047)+ (400*1.046)+ (400*1.045)+ (400*1.044)+(400*1.043)+ (400*1.042)+ (400*1.041)+ (400*1.040) = $3,685.69

We can also calculate by assuming Annual addition is $800, 4 years, 8% interest rate, compound 2 times, make additions at end* of each compounding period.

*note If you do it at the start, you'll end up with $4,010.63

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