In: Finance
Question 1
Mr. Clark made deposits of $950 at the end of every 6 months for 15 years. If interest is 3% compounded monthly and if he leaves the accumulated balance for another 10 years, what will be the balance in his account then? (i.e. 10 years after the last deposit) _______________
How much of the accumulated amount is interest? _____________
Show calculations and calculator inputs
Eeffective 6 Months Rate = ( 1 + r)^n - 1
= ( 1 + 0.0025)^6 - 1
= ( 1.0025^6 ) - 1
= 1.015094 - 1
= 0.015094 i.e 1.5094%
FV aof Annuity after 15 Yeras:
Annuity is series of cash flows that are deposited at regular intervals for specific period of time.
PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods
Particulars | Amount |
Cash Flow | 950 |
Int Rate | 1.509% |
Periods | 30 |
FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r |
= $ 950 * [ [ ( 1 + 0.01509 ) ^ 30 ] - 1 ] / 0.01509 |
= $ 950 * [ [ ( 1.015094 ) ^ 30 ] - 1 ] / 0.015094 |
= $ 950 * [ [1.5674] - 1 ] / 0.015094 |
= $ 950 * [0.5674] /0.015094 |
= $ 35713.35 |
FV after 10 Years :
FV = PV (1+r)^n
Where n is Int rate per period
n - No. of periods
= $ 35713.35 * ( 1 + 0.015094 )^ 20
= $ 35713.35 * ( 1.015094 )^ 20
= $ 35713.35 * 1.3494
= $ 48189.94
Int = FV after 25 Years - [ Deposits Made ]
= $ 48189.94 - [ $ 950 * 30 ]
= $ 48189.94 - [ $ 28500 ]
= $ 19689.94
Pls do rate, if the answer is correct and comment, if any further assistance is required.